KILLED proof of input_jdsuaNz7JW.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 219 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 1 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [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), 14 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 109 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 153 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 156 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 175 ms] (186) CdtProblem (187) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 271 ms] (192) CdtProblem (193) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 165 ms] (198) CdtProblem (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 733 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 728 ms] (212) CdtProblem (213) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1353 ms] (216) CdtProblem (217) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1274 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 46 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1320 ms] (224) CdtProblem (225) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4492 ms] (228) CdtProblem (229) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (230) 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__zeros -> cons(0, zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0 a__length(cons(N, L)) -> s(a__length(mark(L))) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0', zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0' a__length(cons(N, L)) -> s(a__length(mark(L))) a__take(0', IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__and(tt, X) -> mark(X) a__length(nil) -> 0 a__length(cons(N, L)) -> s(a__length(mark(L))) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) mark(zeros) -> a__zeros mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(X)) -> s(mark(X)) a__zeros -> zeros a__and(X1, X2) -> and(X1, X2) a__length(X) -> length(X) a__take(X1, X2) -> take(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] a__take(X1, X2) -> take(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 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__take_2 a__zeros a__and_2 a__length_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, zeros)) -> s(a__length(a__zeros)) [2] a__length(cons(N, and(X1', X2'))) -> s(a__length(a__and(mark(X1'), X2'))) [2] a__length(cons(N, length(X'))) -> s(a__length(a__length(mark(X')))) [2] a__length(cons(N, take(X1'', X2''))) -> s(a__length(a__take(mark(X1''), mark(X2'')))) [2] a__length(cons(N, cons(X11, X21))) -> s(a__length(cons(mark(X11), X21))) [2] a__length(cons(N, 0)) -> s(a__length(0)) [2] a__length(cons(N, tt)) -> s(a__length(tt)) [2] a__length(cons(N, nil)) -> s(a__length(nil)) [2] a__length(cons(N, s(X''))) -> s(a__length(s(mark(X'')))) [2] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(zeros, X2)) -> a__and(a__zeros, X2) [2] mark(and(and(X12, X22), X2)) -> a__and(a__and(mark(X12), X22), X2) [2] mark(and(length(X3), X2)) -> a__and(a__length(mark(X3)), X2) [2] mark(and(take(X13, X23), X2)) -> a__and(a__take(mark(X13), mark(X23)), X2) [2] mark(and(cons(X14, X24), X2)) -> a__and(cons(mark(X14), X24), X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(nil, X2)) -> a__and(nil, X2) [2] mark(and(s(X4), X2)) -> a__and(s(mark(X4)), X2) [2] mark(length(zeros)) -> a__length(a__zeros) [2] mark(length(and(X15, X25))) -> a__length(a__and(mark(X15), X25)) [2] mark(length(length(X5))) -> a__length(a__length(mark(X5))) [2] mark(length(take(X16, X26))) -> a__length(a__take(mark(X16), mark(X26))) [2] mark(length(cons(X17, X27))) -> a__length(cons(mark(X17), X27)) [2] mark(length(0)) -> a__length(0) [2] mark(length(tt)) -> a__length(tt) [2] mark(length(nil)) -> a__length(nil) [2] mark(length(s(X6))) -> a__length(s(mark(X6))) [2] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 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 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> 1 + a__length(a__zeros) :|: z = 1 + N + 3, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z = 1 + N + 2, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z = 1 + N + 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__zeros) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 0 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(X6)) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__length(1 + mark(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 2 }-> a__and(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 0 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (15) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 3 }-> 1 + a__length(3) :|: z = 1 + N + 3, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z = 1 + N + 2, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z = 1 + N + 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 1 + N + 3, N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(X5))) :|: X5 >= 0, z = 1 + (1 + X5) mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 0 mark(z) -{ 3 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(X6)) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__length(1 + mark(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__and(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 0 mark(z) -{ 3 }-> a__and(1 + 0 + 3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 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) -{ 2 }-> 1 + 0 + 3 :|: 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__and(z, z') -{ 1 }-> mark(z') :|: z = 2, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__take(mark(X1''), mark(X2''))) :|: X1'' >= 0, X2'' >= 0, z = 1 + N + (1 + X1'' + X2''), N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 1 + N + (1 + X'), X' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(a__and(mark(X1'), X2')) :|: X2' >= 0, z = 1 + N + (1 + X1' + X2'), X1' >= 0, N >= 0 a__length(z) -{ 3 }-> 1 + a__length(3) :|: z - 4 >= 0 a__length(z) -{ 2 }-> 1 + a__length(2) :|: z - 3 >= 0 a__length(z) -{ 2 }-> 1 + a__length(1) :|: z - 2 >= 0 a__length(z) -{ 2 }-> 1 + a__length(0) :|: z - 1 >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 1 + N + (1 + X''), X'' >= 0, N >= 0 a__length(z) -{ 2 }-> 1 + a__length(1 + mark(X11) + X21) :|: X11 >= 0, X21 >= 0, z = 1 + N + (1 + X11 + X21), N >= 0 a__length(z) -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z - 4 >= 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(N) + (1 + (z - 1) + IL) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__length(a__take(mark(X16), mark(X26))) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(a__and(mark(X15), X25)) :|: z = 1 + (1 + X15 + X25), X15 >= 0, X25 >= 0 mark(z) -{ 3 }-> a__length(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__length(2) :|: z = 1 + 2 mark(z) -{ 2 }-> a__length(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__length(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__length(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X17) + X27) :|: z = 1 + (1 + X17 + X27), X17 >= 0, X27 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__and(a__take(mark(X13), mark(X23)), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__and(a__length(mark(X3)), X2) :|: z = 1 + (1 + X3) + X2, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X12), X22), X2) :|: z = 1 + (1 + X12 + X22) + X2, X12 >= 0, X22 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__and(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__and(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(1 + mark(X4), X2) :|: X4 >= 0, X2 >= 0, z = 1 + (1 + X4) + X2 mark(z) -{ 2 }-> a__and(1 + mark(X14) + X24, X2) :|: z = 1 + (1 + X14 + X24) + X2, X2 >= 0, X14 >= 0, X24 >= 0 mark(z) -{ 3 }-> a__and(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 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) -{ 2 }-> 1 + 0 + 3 :|: 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__zeros -> cons(0, zeros) [1] a__and(tt, X) -> mark(X) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> s(a__length(mark(L))) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL)) [1] mark(zeros) -> a__zeros [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] a__zeros -> zeros [1] a__and(X1, X2) -> and(X1, X2) [1] a__length(X) -> length(X) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:nil:s:take:and:length cons :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 0 :: 0:zeros:cons:tt:nil:s:take:and:length zeros :: 0:zeros:cons:tt:nil:s:take:and:length a__and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length tt :: 0:zeros:cons:tt:nil:s:take:and:length mark :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length nil :: 0:zeros:cons:tt:nil:s:take:and:length s :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length a__take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length take :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length and :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length length :: 0:zeros:cons:tt:nil:s:take:and:length -> 0:zeros:cons:tt:nil:s:take:and:length 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 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 1 }-> 1 + a__length(mark(L)) :|: z = 1 + N + L, L >= 0, N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(MARK(z0)) S tuples: A__ZEROS -> c A__ZEROS -> c1 A__AND(tt, z0) -> c2(MARK(z0)) A__AND(z0, z1) -> c3 A__LENGTH(nil) -> c4 A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__LENGTH(z0) -> c6 A__TAKE(0, z0) -> c7 A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) A__TAKE(z0, z1) -> c9 MARK(zeros) -> c10(A__ZEROS) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(tt) -> c17 MARK(nil) -> c18 MARK(s(z0)) -> c19(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__AND_2, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6, c7, c8_1, c9, c10_1, c11_2, c12_2, c13_2, c14_2, c15_1, c16, c17, c18, c19_1 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 11 trailing nodes: MARK(nil) -> c18 A__LENGTH(z0) -> c6 A__TAKE(0, z0) -> c7 A__LENGTH(nil) -> c4 A__TAKE(z0, z1) -> c9 A__ZEROS -> c MARK(0) -> c16 MARK(zeros) -> c10(A__ZEROS) MARK(tt) -> c17 A__AND(z0, z1) -> c3 A__ZEROS -> c1 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c2_1, c5_2, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1 ---------------------------------------- (27) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c5(A__LENGTH(mark(z1)), MARK(z1)) by A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2 ---------------------------------------- (29) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__LENGTH(cons(x0, 0)) -> c5(A__LENGTH(0), MARK(0)) A__LENGTH(cons(x0, nil)) -> c5(A__LENGTH(nil), MARK(nil)) A__LENGTH(cons(x0, tt)) -> c5(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros), MARK(zeros)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c11_2, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(nil, x1)) -> c11(A__AND(nil, x1), MARK(nil)) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(cons(z0, z1), x1)) -> c11(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c12_2, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1 ---------------------------------------- (39) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c12(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2 ---------------------------------------- (41) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(tt)) -> c12(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c12(A__LENGTH(nil), MARK(nil)) MARK(length(0)) -> c12(A__LENGTH(0), MARK(0)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c13_2, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c13(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(tt, x1)) -> c13(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c13(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(0, x1)) -> c13(A__TAKE(0, mark(x1)), MARK(0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c13(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c13(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, nil)) -> c13(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, s(z0))) -> c13(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c13(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c14_2, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c14(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(x0, tt)) -> c14(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, 0)) -> c14(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, nil)) -> c14(A__TAKE(mark(x0), nil), MARK(nil)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c14(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c14(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c14(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c14(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(z0, z1))) -> c5(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(x1, z1))) -> c5(A__LENGTH(and(mark(x1), z1)), MARK(and(x1, z1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2)), MARK(and(0, x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2)), MARK(and(nil, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(z0))) -> c5(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(x1))) -> c5(A__LENGTH(length(mark(x1))), MARK(length(x1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0)), MARK(length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt)), MARK(length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil)), MARK(length(nil))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, take(z0, z1))) -> c5(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by A__LENGTH(cons(x0, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(A__LENGTH(take(mark(x1), mark(x2))), MARK(take(x1, x2))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(a__zeros)) by A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(zeros)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) by MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(x0, z1), x2)) -> c11(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2), MARK(and(nil, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(length(z0), x1)) -> c11(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(x0), x1)) -> c11(A__AND(length(mark(x0)), x1), MARK(length(x0))) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1), MARK(length(0))) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1), MARK(length(tt))) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1), MARK(length(nil))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(take(z0, z1), x1)) -> c11(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(and(take(x0, x1), x2)) -> c11(A__AND(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, x1), x2)) -> c11(A__AND(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, x1), x2)) -> c11(A__AND(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, 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c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), 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x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> 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mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(zeros, x1)) -> c11(A__AND(a__zeros, x1)) by MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(zeros, x0)) -> c11(A__AND(zeros, x0)) MARK(and(zeros, x0)) -> c11(A__AND(cons(0, zeros), x0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2)), MARK(and(zeros, x2))) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2), MARK(and(zeros, x1))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), 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z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(and(z0, z1))) -> c12(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(length(and(x0, z1))) -> c12(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) 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MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(x0, z1))) -> c12(A__LENGTH(and(mark(x0), z1)), MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1)), MARK(and(zeros, x1))) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1)), MARK(and(0, x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1)), MARK(and(nil, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(z0))) -> c12(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by MARK(length(length(x0))) -> c12(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(x0))) -> c12(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(x0))) -> c12(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil)), MARK(length(nil))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(take(z0, z1))) -> c12(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(length(take(x0, x1))) -> c12(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, x1))) -> c12(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, x1))) -> c12(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(zeros)) -> c12(A__LENGTH(a__zeros)) by MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c12(A__LENGTH(zeros)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c12(A__LENGTH(zeros)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c12(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(zeros)) -> c12(A__LENGTH(zeros)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), a__zeros), MARK(x0)) by MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> 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MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(tt, zeros)) -> c13(A__TAKE(tt, a__zeros), MARK(tt)) MARK(take(nil, zeros)) -> c13(A__TAKE(nil, a__zeros), MARK(nil)) MARK(take(0, zeros)) -> c13(A__TAKE(0, a__zeros), MARK(0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) 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c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), zeros), MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(cons(z0, z1), zeros)) -> c13(A__TAKE(cons(mark(z0), z1), a__zeros), MARK(cons(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), 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take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, and(z0, z1))) -> c13(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), 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c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, 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MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, and(x1, x2))) -> c13(A__TAKE(nil, a__and(mark(x1), x2)), MARK(nil)) MARK(take(tt, and(x1, x2))) -> c13(A__TAKE(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(take(0, and(x1, x2))) -> c13(A__TAKE(0, a__and(mark(x1), x2)), MARK(0)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) 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MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) 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-> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, 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MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(x1, z1))) -> c13(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) 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c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), 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MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, 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MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), 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MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, length(z0))) -> c13(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) by MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), 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MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) 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MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> 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c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, 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z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, length(x1))) -> c13(A__TAKE(nil, a__length(mark(x1))), MARK(nil)) MARK(take(0, length(x1))) -> c13(A__TAKE(0, a__length(mark(x1))), MARK(0)) MARK(take(tt, length(x1))) -> c13(A__TAKE(tt, a__length(mark(x1))), MARK(tt)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> 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length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(x1))) -> c13(A__TAKE(mark(x0), length(mark(x1))), MARK(x0)) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1))), MARK(zeros)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), length(x1))) -> c13(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) 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MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> 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MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), 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c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c13(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) by MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), 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-> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), 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z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), 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MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(0, take(x1, x2))) -> c13(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(tt, take(x1, x2))) -> c13(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(tt)) MARK(take(nil, take(x1, x2))) -> c13(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) 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-> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) 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length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, x2))) -> c13(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(zeros)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) 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MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), 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a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) 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length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c13(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), 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c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, cons(x1, x2))) -> c13(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(tt, cons(x1, x2))) -> c13(A__TAKE(tt, cons(mark(x1), x2)), MARK(tt)) MARK(take(0, cons(x1, x2))) -> c13(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, 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-> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 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c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(zeros)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), 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c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(and(z0, z1), x1)) -> c13(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by MARK(take(and(x0, x1), zeros)) -> c13(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(and(x0, x1))) MARK(take(and(x0, x1), and(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) MARK(take(and(x0, x1), length(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), a__length(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, x1), take(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), a__take(mark(z0), mark(z1))), MARK(and(x0, x1))) MARK(take(and(x0, x1), cons(z0, z1))) -> c13(A__TAKE(a__and(mark(x0), x1), cons(mark(z0), z1)), MARK(and(x0, x1))) MARK(take(and(x0, x1), 0)) -> c13(A__TAKE(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(A__TAKE(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(A__TAKE(a__and(mark(x0), x1), nil), MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(and(zeros, x1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2)), MARK(and(nil, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) 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c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(x0, x1), 0)) -> c13(A__TAKE(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(A__TAKE(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(A__TAKE(a__and(mark(x0), x1), nil), MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(and(zeros, x1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2)), MARK(and(nil, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) 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c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(length(z0), x1)) -> c13(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) by MARK(take(length(x0), zeros)) -> c13(A__TAKE(a__length(mark(x0)), a__zeros), MARK(length(x0))) MARK(take(length(x0), and(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), a__and(mark(z0), z1)), MARK(length(x0))) MARK(take(length(x0), length(z0))) -> c13(A__TAKE(a__length(mark(x0)), a__length(mark(z0))), MARK(length(x0))) MARK(take(length(x0), take(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), a__take(mark(z0), mark(z1))), MARK(length(x0))) MARK(take(length(x0), cons(z0, z1))) -> c13(A__TAKE(a__length(mark(x0)), cons(mark(z0), z1)), MARK(length(x0))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, 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MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> 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MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, 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c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, 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cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(x0), 0)) -> c13(A__TAKE(a__length(mark(x0)), 0), MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(A__TAKE(a__length(mark(x0)), tt), MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(A__TAKE(a__length(mark(x0)), nil), MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(A__TAKE(length(mark(x0)), mark(x1)), MARK(length(x0))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1)), MARK(length(0))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1)), MARK(length(tt))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1)), MARK(length(nil))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> 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c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(take(z0, z1), x1)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) by MARK(take(take(x0, x1), zeros)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(take(x0, x1))) MARK(take(take(x0, x1), and(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(take(x0, x1))) MARK(take(take(x0, x1), length(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__length(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), take(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), cons(z0, z1))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(take(x0, x1))) MARK(take(take(x0, x1), 0)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) 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MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> 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cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, x1), 0)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) 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MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, 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c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, 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A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), 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MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, x1), 0)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) 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c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c11_2 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(s(z0), x1)) -> c13(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(take(s(x0), zeros)) -> c13(A__TAKE(s(mark(x0)), a__zeros), MARK(s(x0))) MARK(take(s(x0), and(z0, z1))) -> c13(A__TAKE(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) MARK(take(s(x0), length(z0))) -> c13(A__TAKE(s(mark(x0)), a__length(mark(z0))), MARK(s(x0))) MARK(take(s(x0), take(z0, z1))) -> c13(A__TAKE(s(mark(x0)), a__take(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(x0), cons(z0, z1))) -> c13(A__TAKE(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> 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a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), 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c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(x0), 0)) -> c13(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(A__TAKE(s(mark(x0)), tt), MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 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c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, 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mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(zeros, x1)) -> c13(A__TAKE(a__zeros, mark(x1))) by MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, and(z0, z1))) -> c13(A__TAKE(a__zeros, a__and(mark(z0), z1))) MARK(take(zeros, length(z0))) -> c13(A__TAKE(a__zeros, a__length(mark(z0)))) MARK(take(zeros, take(z0, z1))) -> c13(A__TAKE(a__zeros, a__take(mark(z0), mark(z1)))) MARK(take(zeros, cons(z0, z1))) -> c13(A__TAKE(a__zeros, cons(mark(z0), z1))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> 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a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), 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MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: MARK(take(zeros, x0)) -> c13(A__TAKE(cons(0, zeros), mark(x0))) MARK(take(zeros, 0)) -> c13(A__TAKE(a__zeros, 0)) MARK(take(zeros, x0)) -> c13(A__TAKE(zeros, mark(x0))) MARK(take(zeros, tt)) -> c13(A__TAKE(a__zeros, tt)) MARK(take(zeros, nil)) -> c13(A__TAKE(a__zeros, nil)) MARK(take(zeros, s(z0))) -> c13(A__TAKE(a__zeros, s(mark(z0)))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) 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c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), 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mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) 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a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, and(z0, z1))) -> c14(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(take(x0, and(x1, z1))) -> c14(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(and(zeros, x2))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2)), MARK(and(nil, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(A__TAKE(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(A__TAKE(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(A__TAKE(nil, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> 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MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> 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c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(x1, z1))) -> c14(A__TAKE(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(and(zeros, x2))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2)), MARK(and(nil, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(A__TAKE(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(A__TAKE(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(A__TAKE(nil, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), 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c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), 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c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, 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c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) 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z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, length(z0))) -> c14(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) by MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> 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c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), 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mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), 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x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(x1))) -> c14(A__TAKE(mark(x0), length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0)), MARK(length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt)), MARK(length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil)), MARK(length(nil))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(cons(z0, z1), length(x1))) -> c14(A__TAKE(cons(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(0, length(x1))) -> c14(A__TAKE(0, a__length(mark(x1))), MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(A__TAKE(tt, a__length(mark(x1))), MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(A__TAKE(nil, a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> 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MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> 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c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c14(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(take(x0, take(x1, x2))) -> c14(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, 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a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, x2))) -> c14(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(A__TAKE(tt, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), 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c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), 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-> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c14(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, 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x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> 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c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(A__TAKE(tt, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), 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MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), 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MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> 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a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(zeros, x1)) -> c14(A__TAKE(a__zeros, mark(x1)), MARK(x1)) by MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, and(z0, z1))) -> c14(A__TAKE(a__zeros, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(zeros, length(z0))) -> c14(A__TAKE(a__zeros, a__length(mark(z0))), MARK(length(z0))) MARK(take(zeros, take(z0, z1))) -> c14(A__TAKE(a__zeros, a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(zeros, cons(z0, z1))) -> c14(A__TAKE(a__zeros, cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), 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-> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, 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c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(zeros, nil)) -> c14(A__TAKE(a__zeros, nil), MARK(nil)) MARK(take(zeros, tt)) -> c14(A__TAKE(a__zeros, tt), MARK(tt)) MARK(take(zeros, 0)) -> c14(A__TAKE(a__zeros, 0), MARK(0)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) 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c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), 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MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) 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MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 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a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros), MARK(zeros)) MARK(take(zeros, s(z0))) -> c14(A__TAKE(a__zeros, s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x0)) -> c14(A__TAKE(cons(0, zeros), mark(x0)), MARK(x0)) MARK(take(zeros, x0)) -> c14(A__TAKE(zeros, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, 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c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, 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A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), 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c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), 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z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(and(z0, z1), x1)) -> c14(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), and(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(and(x0, x1), length(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), a__length(mark(z0))), MARK(length(z0))) MARK(take(and(x0, x1), take(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(and(x0, x1), cons(z0, z1))) -> c14(A__TAKE(a__and(mark(x0), x1), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), 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c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) 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MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, 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a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> 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MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, 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c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(and(x0, x1), tt)) -> c14(A__TAKE(a__and(mark(x0), x1), tt), MARK(tt)) MARK(take(and(x0, x1), nil)) -> c14(A__TAKE(a__and(mark(x0), x1), nil), MARK(nil)) MARK(take(and(x0, x1), 0)) -> c14(A__TAKE(a__and(mark(x0), x1), 0), MARK(0)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> 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c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, 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cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros), MARK(zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(A__TAKE(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(A__TAKE(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> 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MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> 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z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(length(z0), x1)) -> c14(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) by MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), and(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(length(x0), length(z0))) -> c14(A__TAKE(a__length(mark(x0)), a__length(mark(z0))), MARK(length(z0))) MARK(take(length(x0), take(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(length(x0), cons(z0, z1))) -> c14(A__TAKE(a__length(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, 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c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (187) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(length(x0), 0)) -> c14(A__TAKE(a__length(mark(x0)), 0), MARK(0)) MARK(take(length(x0), nil)) -> c14(A__TAKE(a__length(mark(x0)), nil), MARK(nil)) MARK(take(length(x0), tt)) -> c14(A__TAKE(a__length(mark(x0)), tt), MARK(tt)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> 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c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> 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c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros), MARK(zeros)) MARK(take(length(x0), s(z0))) -> c14(A__TAKE(a__length(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(A__TAKE(length(mark(x0)), mark(x1)), MARK(x1)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> 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MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, 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mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, 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x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) 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MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(take(z0, z1), x1)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(zeros)) MARK(take(take(x0, x1), and(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(take(x0, x1), length(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__length(mark(z0))), MARK(length(z0))) MARK(take(take(x0, x1), take(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(take(x0, x1), cons(z0, z1))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) MARK(take(take(x0, x1), s(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), 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z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), 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MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros), MARK(zeros)) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) MARK(take(take(x0, x1), s(z0))) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (193) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(take(x0, x1), tt)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), tt), MARK(tt)) MARK(take(take(x0, x1), 0)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(0)) MARK(take(take(x0, x1), nil)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(nil)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> 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c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) 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c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) 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c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), 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c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> 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c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), 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c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_2, c14_1, c11_2, c13_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(s(z0), x1)) -> c14(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), and(z0, z1))) -> c14(A__TAKE(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(s(x0), length(z0))) -> c14(A__TAKE(s(mark(x0)), a__length(mark(z0))), MARK(length(z0))) MARK(take(s(x0), take(z0, z1))) -> c14(A__TAKE(s(mark(x0)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(s(x0), cons(z0, z1))) -> c14(A__TAKE(s(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> 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MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(s(x0), 0)) -> c14(A__TAKE(s(mark(x0)), 0), MARK(0)) MARK(take(s(x0), nil)) -> c14(A__TAKE(s(mark(x0)), nil), MARK(nil)) MARK(take(s(x0), tt)) -> c14(A__TAKE(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), 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MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> 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MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), 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MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros), MARK(zeros)) MARK(take(s(x0), s(z0))) -> c14(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), 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c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), a__zeros)) by MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(and(z0, z1), zeros)) -> c14(A__TAKE(a__and(mark(z0), z1), a__zeros)) MARK(take(length(z0), zeros)) -> c14(A__TAKE(a__length(mark(z0)), a__zeros)) MARK(take(take(z0, z1), zeros)) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) MARK(take(s(z0), zeros)) -> c14(A__TAKE(s(mark(z0)), a__zeros)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> 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x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), 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MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: MARK(take(nil, zeros)) -> c14(A__TAKE(nil, a__zeros)) MARK(take(tt, zeros)) -> c14(A__TAKE(tt, a__zeros)) MARK(take(0, zeros)) -> c14(A__TAKE(0, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c14(A__TAKE(cons(mark(z0), z1), a__zeros)) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), zeros)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) 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MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), 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cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(0, x2))) -> c5(A__LENGTH(a__and(0, x2))) by A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) 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MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(0, z1))) -> c5(A__LENGTH(and(0, z1))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) 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MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(take(x0, length(cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(take(x0, length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, and(nil, x2))) -> c5(A__LENGTH(a__and(nil, x2))) by A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) 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MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (213) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, and(nil, z1))) -> c5(A__LENGTH(and(nil, z1))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), 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c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> 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c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(a__length(0))) by A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> 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mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (217) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(0))) -> c5(A__LENGTH(length(0))) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> 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A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), 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MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> 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length(s(z0)))) -> c14(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(take(zeros, length(x1))) -> c14(A__TAKE(a__zeros, a__length(mark(x1))), MARK(length(x1))) MARK(take(and(z0, z1), length(x1))) -> c14(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(length(x1))) MARK(take(length(z0), length(x1))) -> c14(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(take(z0, z1), length(x1))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(length(x1))) MARK(take(s(z0), length(x1))) -> c14(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(length(x1))) MARK(take(x0, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, length(0))) -> c14(A__TAKE(mark(x0), a__length(0))) MARK(take(x0, length(tt))) -> c14(A__TAKE(mark(x0), a__length(tt))) MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(a__length(tt))) by A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, and(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(0, x2))) -> c13(A__TAKE(mark(x0), a__and(0, x2)), MARK(x0)) MARK(take(x0, and(tt, x2))) -> c13(A__TAKE(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(take(x0, and(nil, x2))) -> c13(A__TAKE(mark(x0), a__and(nil, x2)), MARK(x0)) MARK(take(x0, and(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), and(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), and(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), and(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(take(x0, and(x1, z1))) -> c13(MARK(x0)) MARK(take(zeros, and(x1, x2))) -> c13(A__TAKE(a__zeros, a__and(mark(x1), x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, length(zeros))) -> c13(A__TAKE(mark(x0), a__length(a__zeros)), MARK(x0)) MARK(take(x0, length(and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(length(z0)))) -> c13(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(x0)) MARK(take(x0, length(take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, length(cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__length(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, length(0))) -> c13(A__TAKE(mark(x0), a__length(0)), MARK(x0)) MARK(take(x0, length(tt))) -> c13(A__TAKE(mark(x0), a__length(tt)), MARK(x0)) MARK(take(x0, length(nil))) -> c13(A__TAKE(mark(x0), a__length(nil)), MARK(x0)) MARK(take(x0, length(s(z0)))) -> c13(A__TAKE(mark(x0), a__length(s(mark(z0)))), MARK(x0)) MARK(take(and(z0, z1), length(x1))) -> c13(A__TAKE(a__and(mark(z0), z1), a__length(mark(x1))), MARK(and(z0, z1))) MARK(take(length(z0), length(x1))) -> c13(A__TAKE(a__length(mark(z0)), a__length(mark(x1))), MARK(length(z0))) MARK(take(take(z0, z1), length(x1))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__length(mark(x1))), MARK(take(z0, z1))) MARK(take(s(z0), length(x1))) -> c13(A__TAKE(s(mark(z0)), a__length(mark(x1))), MARK(s(z0))) MARK(take(x0, length(x1))) -> c13(MARK(x0)) MARK(take(zeros, length(x1))) -> c13(A__TAKE(a__zeros, a__length(mark(x1)))) MARK(take(cons(z0, z1), length(x1))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, take(x1, zeros))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(x0)) MARK(take(x0, take(x1, and(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, length(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, tt))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c13(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(zeros, x2))) -> c13(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(x0)) MARK(take(x0, take(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c13(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(tt, x2))) -> c13(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c13(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c13(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(and(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(take(length(z0), take(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(length(z0))) MARK(take(take(z0, z1), take(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c13(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c13(MARK(x0)) MARK(take(zeros, take(x1, x2))) -> c13(A__TAKE(a__zeros, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(x0, cons(zeros, x2))) -> c13(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(x0)) MARK(take(x0, cons(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(length(z0), x2))) -> c13(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c13(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c13(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(tt, x2))) -> c13(A__TAKE(mark(x0), cons(tt, x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c13(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c13(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(and(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(and(z0, z1))) MARK(take(length(z0), cons(x1, x2))) -> c13(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(length(z0))) MARK(take(take(z0, z1), cons(x1, x2))) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c13(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(zeros, cons(x1, x2))) -> c13(A__TAKE(a__zeros, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c13(MARK(cons(z0, z1))) MARK(take(and(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(take(and(length(z0), x1), x2)) -> c13(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(and(length(z0), x1))) MARK(take(and(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(take(z0, z1), x1))) MARK(take(and(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(and(cons(z0, z1), x1))) MARK(take(and(tt, x1), x2)) -> c13(A__TAKE(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(take(and(s(z0), x1), x2)) -> c13(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(take(and(x0, x1), 0)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), tt)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), nil)) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, x1), s(z0))) -> c13(MARK(and(x0, x1))) MARK(take(and(x0, z1), x2)) -> c13(MARK(and(x0, z1))) MARK(take(and(zeros, x1), x2)) -> c13(A__TAKE(a__and(a__zeros, x1), mark(x2))) MARK(take(and(0, x1), x2)) -> c13(A__TAKE(a__and(0, x1), mark(x2))) MARK(take(and(nil, x1), x2)) -> c13(A__TAKE(a__and(nil, x1), mark(x2))) MARK(take(length(zeros), x1)) -> c13(A__TAKE(a__length(a__zeros), mark(x1)), MARK(length(zeros))) MARK(take(length(and(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(length(and(z0, z1)))) MARK(take(length(length(z0)), x1)) -> c13(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(length(length(z0)))) MARK(take(length(take(z0, z1)), x1)) -> c13(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(length(take(z0, z1)))) MARK(take(length(cons(z0, z1)), x1)) -> c13(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(length(cons(z0, z1)))) MARK(take(length(s(z0)), x1)) -> c13(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(length(s(z0)))) MARK(take(length(x0), 0)) -> c13(MARK(length(x0))) MARK(take(length(x0), tt)) -> c13(MARK(length(x0))) MARK(take(length(x0), nil)) -> c13(MARK(length(x0))) MARK(take(length(x0), s(z0))) -> c13(MARK(length(x0))) MARK(take(length(x0), x1)) -> c13(MARK(length(x0))) MARK(take(length(0), x1)) -> c13(A__TAKE(a__length(0), mark(x1))) MARK(take(length(tt), x1)) -> c13(A__TAKE(a__length(tt), mark(x1))) MARK(take(length(nil), x1)) -> c13(A__TAKE(a__length(nil), mark(x1))) MARK(take(take(x0, zeros), x2)) -> c13(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(take(x0, zeros))) MARK(take(take(x0, and(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(take(x0, and(z0, z1)))) MARK(take(take(x0, length(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> c13(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(take(length(z0), x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c13(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(tt, x1), x2)) -> c13(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(take(tt, x1))) MARK(take(take(nil, x1), x2)) -> c13(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(s(z0), x1), x2)) -> c13(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(x0, x1), 0)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), tt)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c13(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c13(MARK(take(x0, x1))) MARK(take(s(zeros), x1)) -> c13(A__TAKE(s(a__zeros), mark(x1)), MARK(s(zeros))) MARK(take(s(and(z0, z1)), x1)) -> c13(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(take(s(length(z0)), x1)) -> c13(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(s(length(z0)))) MARK(take(s(take(z0, z1)), x1)) -> c13(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(cons(z0, z1)), x1)) -> c13(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c13(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(tt), x1)) -> c13(A__TAKE(s(tt), mark(x1)), MARK(s(tt))) MARK(take(s(nil), x1)) -> c13(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(s(z0)), x1)) -> c13(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(x0), x1)) -> c13(MARK(s(x0))) MARK(take(s(x0), 0)) -> c13(MARK(s(x0))) MARK(take(s(x0), tt)) -> c13(MARK(s(x0))) MARK(take(s(x0), nil)) -> c13(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c13(MARK(s(x0))) MARK(take(x0, and(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(take(x0, and(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) MARK(take(x0, and(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) MARK(take(x0, and(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) MARK(take(x0, and(tt, x2))) -> c14(A__TAKE(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(take(x0, and(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(take(zeros, and(x1, x2))) -> c14(A__TAKE(a__zeros, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(and(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(length(z0), and(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(take(z0, z1), and(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(s(z0), and(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), 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MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__LENGTH(cons(x0, length(tt))) -> c5(A__LENGTH(length(tt))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) 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MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), 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MARK(take(x0, length(z0)))) MARK(take(take(x0, take(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c13(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c13(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, tt), x2)) -> c13(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(take(x0, tt))) MARK(take(take(x0, nil), x2)) -> c13(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, s(z0)), x2)) -> c13(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(zeros, x1), x2)) -> c13(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(take(zeros, x1))) MARK(take(take(and(z0, z1), x1), x2)) -> c13(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(and(z0, z1), x1))) MARK(take(take(length(z0), x1), x2)) -> 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MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), 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x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(a__length(nil))) by A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), 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c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, 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c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, 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c14(A__TAKE(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(take(x0, and(x1, z1))) -> c14(MARK(and(x1, z1))) MARK(take(x0, and(zeros, x2))) -> c14(A__TAKE(mark(x0), a__and(a__zeros, x2))) MARK(take(x0, and(0, x2))) -> c14(A__TAKE(mark(x0), a__and(0, x2))) MARK(take(x0, and(nil, x2))) -> c14(A__TAKE(mark(x0), a__and(nil, x2))) MARK(take(cons(z0, z1), and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(0, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(tt, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(nil, and(x1, x2))) -> c14(MARK(and(x1, x2))) MARK(take(x0, length(zeros))) -> c14(A__TAKE(mark(x0), a__length(a__zeros)), MARK(length(zeros))) MARK(take(x0, length(and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(take(x0, length(length(z0)))) -> c14(A__TAKE(mark(x0), a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(take(x0, length(take(z0, z1)))) -> c14(A__TAKE(mark(x0), a__length(a__take(mark(z0), 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MARK(take(x0, length(nil))) -> c14(A__TAKE(mark(x0), a__length(nil))) MARK(take(cons(z0, z1), length(x1))) -> c14(MARK(length(x1))) MARK(take(0, length(x1))) -> c14(MARK(length(x1))) MARK(take(tt, length(x1))) -> c14(MARK(length(x1))) MARK(take(nil, length(x1))) -> c14(MARK(length(x1))) MARK(take(x0, take(x1, zeros))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) MARK(take(x0, take(x1, and(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (225) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(0)) A__LENGTH(cons(x0, length(nil))) -> c5(A__LENGTH(length(nil))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(and(take(nil, x1), x2)) -> c11(A__AND(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(and(take(s(z0), x1), x2)) -> c11(A__AND(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(and(take(x0, x1), x2)) -> c11(MARK(take(x0, x1))) A__LENGTH(cons(x0, and(zeros, x2))) -> c5(A__LENGTH(a__and(a__zeros, x2))) MARK(and(and(zeros, x1), x2)) -> c11(A__AND(a__and(a__zeros, x1), x2)) MARK(length(and(and(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) MARK(length(and(length(z0), x1))) -> c12(A__LENGTH(a__and(a__length(mark(z0)), x1)), MARK(and(length(z0), x1))) MARK(length(and(take(z0, z1), x1))) -> c12(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x1)), MARK(and(take(z0, z1), x1))) MARK(length(and(cons(z0, z1), x1))) -> c12(A__LENGTH(a__and(cons(mark(z0), z1), x1)), MARK(and(cons(z0, z1), x1))) MARK(length(and(tt, x1))) -> c12(A__LENGTH(a__and(tt, x1)), MARK(and(tt, x1))) MARK(length(and(s(z0), x1))) -> c12(A__LENGTH(a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) MARK(length(and(x0, z1))) -> c12(MARK(and(x0, z1))) MARK(length(and(zeros, x1))) -> c12(A__LENGTH(a__and(a__zeros, x1))) MARK(length(and(0, x1))) -> c12(A__LENGTH(a__and(0, x1))) MARK(length(and(nil, x1))) -> c12(A__LENGTH(a__and(nil, x1))) MARK(length(length(zeros))) -> c12(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(and(z0, z1)))) -> c12(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) MARK(length(length(length(z0)))) -> c12(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(take(z0, z1)))) -> c12(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c12(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c12(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c12(MARK(length(x0))) MARK(length(length(0))) -> c12(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c12(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c12(A__LENGTH(a__length(nil))) MARK(length(take(x0, zeros))) -> c12(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, and(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__and(mark(z0), z1))), MARK(take(x0, and(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c12(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, take(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(length(take(x0, cons(z0, z1)))) -> c12(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c12(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c12(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, nil))) -> c12(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(x0, s(z0)))) -> c12(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(zeros, x1))) -> c12(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(and(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x1))), MARK(take(and(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c12(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(take(z0, z1), x1))) -> c12(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(length(take(cons(z0, z1), x1))) -> c12(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c12(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c12(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(nil, x1))) -> c12(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(s(z0), x1))) -> c12(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(x0, x1))) -> c12(MARK(take(x0, x1))) MARK(length(zeros)) -> c12(A__LENGTH(cons(0, zeros))) MARK(take(x0, zeros)) -> c13(A__TAKE(mark(x0), cons(0, zeros)), MARK(x0)) MARK(take(and(z0, z1), zeros)) -> c13(A__TAKE(a__and(mark(z0), z1), a__zeros), MARK(and(z0, z1))) MARK(take(length(z0), zeros)) -> c13(A__TAKE(a__length(mark(z0)), a__zeros), MARK(length(z0))) MARK(take(take(z0, z1), zeros)) -> c13(A__TAKE(a__take(mark(z0), mark(z1)), a__zeros), MARK(take(z0, z1))) MARK(take(s(z0), zeros)) -> c13(A__TAKE(s(mark(z0)), a__zeros), MARK(s(z0))) MARK(take(x0, zeros)) -> c13(MARK(x0)) MARK(take(zeros, zeros)) -> c13(A__TAKE(a__zeros, a__zeros)) MARK(take(cons(z0, z1), zeros)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, and(zeros, x2))) -> c13(A__TAKE(mark(x0), a__and(a__zeros, x2)), MARK(x0)) MARK(take(x0, and(and(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, and(length(z0), x2))) -> c13(A__TAKE(mark(x0), a__and(a__length(mark(z0)), x2)), MARK(x0)) MARK(take(x0, and(take(z0, z1), x2))) -> c13(A__TAKE(mark(x0), a__and(a__take(mark(z0), mark(z1)), x2)), 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c14(A__TAKE(mark(x0), a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) MARK(take(x0, take(x1, length(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) MARK(take(x0, take(x1, take(z0, z1)))) -> c14(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, cons(z0, z1)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, tt))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), tt)), MARK(take(x1, tt))) MARK(take(x0, take(x1, nil))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, s(z0)))) -> c14(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(zeros, x2))) -> c14(A__TAKE(mark(x0), a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) MARK(take(x0, take(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) MARK(take(x0, take(length(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c14(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(tt, x2))) -> c14(A__TAKE(mark(x0), a__take(tt, mark(x2))), MARK(take(tt, x2))) MARK(take(x0, take(nil, x2))) -> c14(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(s(z0), x2))) -> c14(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(zeros, take(x1, x2))) -> c14(A__TAKE(a__zeros, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(and(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(length(z0), take(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c14(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(tt, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), 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c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) S tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), 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x2))) -> c14(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c14(MARK(take(x1, x2))) MARK(take(x0, cons(zeros, x2))) -> c14(A__TAKE(mark(x0), cons(a__zeros, x2)), MARK(cons(zeros, x2))) MARK(take(x0, cons(and(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__and(mark(z0), z1), x2)), MARK(cons(and(z0, z1), x2))) MARK(take(x0, cons(length(z0), x2))) -> c14(A__TAKE(mark(x0), cons(a__length(mark(z0)), x2)), MARK(cons(length(z0), x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c14(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c14(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(tt, x2))) -> c14(A__TAKE(mark(x0), cons(tt, x2)), MARK(cons(tt, x2))) MARK(take(x0, cons(nil, x2))) -> c14(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(s(z0), x2))) -> c14(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(zeros, cons(x1, x2))) -> c14(A__TAKE(a__zeros, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(and(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__and(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(length(z0), cons(x1, x2))) -> c14(A__TAKE(a__length(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c14(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c14(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(tt, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c14(MARK(cons(x1, x2))) MARK(take(zeros, zeros)) -> c14(A__TAKE(a__zeros, a__zeros)) MARK(take(zeros, s(z0))) -> c14(MARK(s(z0))) MARK(take(zeros, x0)) -> c14(MARK(x0)) MARK(take(and(zeros, x1), x2)) -> c14(A__TAKE(a__and(a__zeros, x1), mark(x2)), MARK(x2)) MARK(take(and(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(length(z0), x1), x2)) -> c14(A__TAKE(a__and(a__length(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(a__take(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(take(and(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__and(cons(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(take(and(0, x1), x2)) -> c14(A__TAKE(a__and(0, x1), mark(x2)), MARK(x2)) MARK(take(and(tt, x1), x2)) -> c14(A__TAKE(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(take(and(nil, x1), x2)) -> c14(A__TAKE(a__and(nil, x1), mark(x2)), MARK(x2)) MARK(take(and(s(z0), x1), x2)) -> c14(A__TAKE(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(take(and(x0, x1), zeros)) -> c14(A__TAKE(a__and(mark(x0), x1), a__zeros)) MARK(take(and(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(and(x0, z1), x2)) -> c14(MARK(x2)) MARK(take(length(zeros), x1)) -> c14(A__TAKE(a__length(a__zeros), mark(x1)), MARK(x1)) MARK(take(length(and(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(length(z0)), x1)) -> c14(A__TAKE(a__length(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(take(z0, z1)), x1)) -> c14(A__TAKE(a__length(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(length(cons(z0, z1)), x1)) -> c14(A__TAKE(a__length(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(length(0), x1)) -> c14(A__TAKE(a__length(0), mark(x1)), MARK(x1)) MARK(take(length(tt), x1)) -> c14(A__TAKE(a__length(tt), mark(x1)), MARK(x1)) MARK(take(length(nil), x1)) -> c14(A__TAKE(a__length(nil), mark(x1)), MARK(x1)) MARK(take(length(s(z0)), x1)) -> c14(A__TAKE(a__length(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(length(x0), zeros)) -> c14(A__TAKE(a__length(mark(x0)), a__zeros)) MARK(take(length(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(length(x0), x1)) -> c14(MARK(x1)) MARK(take(take(x0, zeros), x2)) -> c14(A__TAKE(a__take(mark(x0), a__zeros), mark(x2)), MARK(x2)) MARK(take(take(x0, and(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(0, x1), x2)) -> c11(A__AND(a__and(0, x1), x2)) by MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), 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MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) 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MARK(take(take(x0, length(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__length(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(x0, take(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(take(take(x0, cons(z0, z1)), x2)) -> c14(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(take(take(x0, 0), x2)) -> c14(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(x2)) MARK(take(take(x0, tt), x2)) -> c14(A__TAKE(a__take(mark(x0), tt), mark(x2)), MARK(x2)) MARK(take(take(x0, nil), x2)) -> c14(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(x2)) MARK(take(take(x0, s(z0)), x2)) -> c14(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(take(take(zeros, x1), x2)) -> c14(A__TAKE(a__take(a__zeros, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(and(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(length(z0), x1), x2)) -> c14(A__TAKE(a__take(a__length(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(take(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(cons(z0, z1), x1), x2)) -> c14(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(0, x1), x2)) -> c14(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(tt, x1), x2)) -> c14(A__TAKE(a__take(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(nil, x1), x2)) -> c14(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(x0), zeros)) -> c14(A__TAKE(s(mark(x0)), a__zeros)) MARK(take(s(x0), s(z0))) -> c14(MARK(s(z0))) MARK(take(x0, zeros)) -> c14(A__TAKE(mark(x0), cons(0, zeros))) MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__and_2, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__AND_2, A__TAKE_2, MARK_1, A__LENGTH_1 Compound Symbols: c2_1, c8_1, c15_1, c19_1, c5_2, c5_1, c11_1, c12_2, c12_1, c13_1, c14_1, c11_2, c13_2, c14_2 ---------------------------------------- (229) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(0, z1), x1)) -> c11(A__AND(and(0, z1), x1)) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__length(nil) -> 0 a__length(cons(z0, z1)) -> s(a__length(mark(z1))) a__length(z0) -> length(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) mark(zeros) -> a__zeros mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c2(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c8(MARK(z1)) MARK(cons(z0, z1)) -> c15(MARK(z0)) MARK(s(z0)) -> c19(MARK(z0)) A__LENGTH(cons(x0, cons(z0, z1))) -> c5(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__LENGTH(cons(x0, s(z0))) -> c5(MARK(s(z0))) MARK(and(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c12(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c12(MARK(s(z0))) MARK(take(x0, 0)) -> c13(MARK(x0)) MARK(take(x0, tt)) -> c13(MARK(x0)) MARK(take(x0, nil)) -> c13(MARK(x0)) MARK(take(x0, s(z0))) -> c13(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c13(MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c14(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c14(MARK(x1)) MARK(take(0, x1)) -> c14(MARK(x1)) MARK(take(tt, x1)) -> c14(MARK(x1)) MARK(take(nil, x1)) -> c14(MARK(x1)) A__LENGTH(cons(x0, and(and(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__LENGTH(cons(x0, and(length(z0), x2))) -> c5(A__LENGTH(a__and(a__length(mark(z0)), x2)), MARK(and(length(z0), x2))) A__LENGTH(cons(x0, and(take(z0, z1), x2))) -> c5(A__LENGTH(a__and(a__take(mark(z0), mark(z1)), x2)), MARK(and(take(z0, z1), x2))) A__LENGTH(cons(x0, and(cons(z0, z1), x2))) -> c5(A__LENGTH(a__and(cons(mark(z0), z1), x2)), MARK(and(cons(z0, z1), x2))) A__LENGTH(cons(x0, and(tt, x2))) -> c5(A__LENGTH(a__and(tt, x2)), MARK(and(tt, x2))) A__LENGTH(cons(x0, and(s(z0), x2))) -> c5(A__LENGTH(a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__LENGTH(cons(x0, and(x1, z1))) -> c5(MARK(and(x1, z1))) A__LENGTH(cons(x0, length(zeros))) -> c5(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__LENGTH(cons(x0, length(and(z0, z1)))) -> c5(A__LENGTH(a__length(a__and(mark(z0), z1))), MARK(length(and(z0, z1)))) A__LENGTH(cons(x0, length(length(z0)))) -> c5(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__LENGTH(cons(x0, length(take(z0, z1)))) -> c5(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__LENGTH(cons(x0, length(cons(z0, z1)))) -> c5(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__LENGTH(cons(x0, length(s(z0)))) -> c5(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__LENGTH(cons(x0, length(x1))) -> c5(MARK(length(x1))) A__LENGTH(cons(x0, take(x1, zeros))) -> c5(A__LENGTH(a__take(mark(x1), a__zeros)), MARK(take(x1, zeros))) A__LENGTH(cons(x0, take(x1, and(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__and(mark(z0), z1))), MARK(take(x1, and(z0, z1)))) A__LENGTH(cons(x0, take(x1, length(z0)))) -> c5(A__LENGTH(a__take(mark(x1), a__length(mark(z0)))), MARK(take(x1, length(z0)))) A__LENGTH(cons(x0, take(x1, take(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) A__LENGTH(cons(x0, take(x1, cons(z0, z1)))) -> c5(A__LENGTH(a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) A__LENGTH(cons(x0, take(x1, 0))) -> c5(A__LENGTH(a__take(mark(x1), 0)), MARK(take(x1, 0))) A__LENGTH(cons(x0, take(x1, tt))) -> c5(A__LENGTH(a__take(mark(x1), tt)), MARK(take(x1, tt))) A__LENGTH(cons(x0, take(x1, nil))) -> c5(A__LENGTH(a__take(mark(x1), nil)), MARK(take(x1, nil))) A__LENGTH(cons(x0, take(x1, s(z0)))) -> c5(A__LENGTH(a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) A__LENGTH(cons(x0, take(zeros, x2))) -> c5(A__LENGTH(a__take(a__zeros, mark(x2))), MARK(take(zeros, x2))) A__LENGTH(cons(x0, take(and(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__and(mark(z0), z1), mark(x2))), MARK(take(and(z0, z1), x2))) A__LENGTH(cons(x0, take(length(z0), x2))) -> c5(A__LENGTH(a__take(a__length(mark(z0)), mark(x2))), MARK(take(length(z0), x2))) A__LENGTH(cons(x0, take(take(z0, z1), x2))) -> c5(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) A__LENGTH(cons(x0, take(cons(z0, z1), x2))) -> c5(A__LENGTH(a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) A__LENGTH(cons(x0, take(0, x2))) -> c5(A__LENGTH(a__take(0, mark(x2))), MARK(take(0, x2))) A__LENGTH(cons(x0, take(tt, x2))) -> c5(A__LENGTH(a__take(tt, mark(x2))), MARK(take(tt, x2))) A__LENGTH(cons(x0, take(nil, x2))) -> c5(A__LENGTH(a__take(nil, mark(x2))), MARK(take(nil, x2))) A__LENGTH(cons(x0, take(s(z0), x2))) -> c5(A__LENGTH(a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) A__LENGTH(cons(x0, take(x1, x2))) -> c5(MARK(take(x1, x2))) A__LENGTH(cons(x0, zeros)) -> c5(A__LENGTH(cons(0, zeros))) MARK(and(and(and(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(length(z0), x1), x2)) -> c11(A__AND(a__and(a__length(mark(z0)), x1), x2), MARK(and(length(z0), x1))) MARK(and(and(take(z0, z1), x1), x2)) -> c11(A__AND(a__and(a__take(mark(z0), mark(z1)), x1), x2), MARK(and(take(z0, z1), x1))) MARK(and(and(cons(z0, z1), x1), x2)) -> c11(A__AND(a__and(cons(mark(z0), z1), x1), x2), MARK(and(cons(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c11(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c11(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c11(MARK(and(x0, z1))) MARK(and(and(nil, x1), x2)) -> c11(A__AND(a__and(nil, x1), x2)) MARK(and(length(zeros), x1)) -> c11(A__AND(a__length(a__zeros), x1), MARK(length(zeros))) MARK(and(length(and(z0, z1)), x1)) -> c11(A__AND(a__length(a__and(mark(z0), z1)), x1), MARK(length(and(z0, z1)))) MARK(and(length(length(z0)), x1)) -> c11(A__AND(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(and(length(take(z0, z1)), x1)) -> c11(A__AND(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(and(length(cons(z0, z1)), x1)) -> c11(A__AND(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(and(length(s(z0)), x1)) -> c11(A__AND(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(and(length(x0), x1)) -> c11(MARK(length(x0))) MARK(and(length(0), x1)) -> c11(A__AND(a__length(0), x1)) MARK(and(length(tt), x1)) -> c11(A__AND(a__length(tt), x1)) MARK(and(length(nil), x1)) -> c11(A__AND(a__length(nil), x1)) MARK(and(take(x0, zeros), x2)) -> c11(A__AND(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(and(take(x0, and(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__and(mark(z0), z1)), x2), MARK(take(x0, and(z0, z1)))) MARK(and(take(x0, length(z0)), x2)) -> c11(A__AND(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(and(take(x0, take(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(and(take(x0, cons(z0, z1)), x2)) -> c11(A__AND(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(and(take(x0, 0), x2)) -> c11(A__AND(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(and(take(x0, tt), x2)) -> c11(A__AND(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(and(take(x0, nil), x2)) -> c11(A__AND(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(and(take(x0, s(z0)), x2)) -> c11(A__AND(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(and(take(zeros, x1), x2)) -> c11(A__AND(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(and(take(and(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__and(mark(z0), z1), mark(x1)), x2), MARK(take(and(z0, z1), x1))) MARK(and(take(length(z0), x1), x2)) -> c11(A__AND(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(and(take(take(z0, z1), x1), x2)) -> c11(A__AND(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(and(take(cons(z0, z1), x1), x2)) -> c11(A__AND(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(and(take(0, x1), x2)) -> c11(A__AND(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(and(take(tt, x1), x2)) -> c11(A__AND(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) 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MARK(take(take(s(z0), x1), x2)) -> c14(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(take(take(x0, x1), zeros)) -> c14(A__TAKE(a__take(mark(x0), mark(x1)), a__zeros)) MARK(take(take(x0, x1), s(z0))) -> c14(MARK(s(z0))) MARK(take(take(x0, x1), x2)) -> c14(MARK(x2)) MARK(take(s(zeros), x1)) -> c14(A__TAKE(s(a__zeros), mark(x1)), MARK(x1)) MARK(take(s(and(z0, z1)), x1)) -> c14(A__TAKE(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(length(z0)), x1)) -> c14(A__TAKE(s(a__length(mark(z0))), mark(x1)), MARK(x1)) MARK(take(s(take(z0, z1)), x1)) -> c14(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(s(cons(z0, z1)), x1)) -> c14(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(s(0), x1)) -> c14(A__TAKE(s(0), mark(x1)), MARK(x1)) MARK(take(s(tt), x1)) -> c14(A__TAKE(s(tt), mark(x1)), MARK(x1)) MARK(take(s(nil), x1)) -> c14(A__TAKE(s(nil), mark(x1)), MARK(x1)) MARK(take(s(s(z0)), x1)) -> c14(A__TAKE(s(s(mark(z0))), mark(x1)), 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