KILLED proof of input_q7B4COHftr.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 27 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 32 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 402 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 2 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtLeafRemovalProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 130 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (210) CdtProblem (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 23 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (216) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0' a__length(cons(N, L)) -> a__U11(tt, L) a__take(0', IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) 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(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 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__U21_4 a__length_1 a__U22_4 a__U23_4 a__U12_2 a__take_2 a__U11_2 a__zeros 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, zeros) -> s(a__length(a__zeros)) [2] a__U12(tt, U11(X1', X2')) -> s(a__length(a__U11(mark(X1'), X2'))) [2] a__U12(tt, U12(X1'', X2'')) -> s(a__length(a__U12(mark(X1''), X2''))) [2] a__U12(tt, length(X')) -> s(a__length(a__length(mark(X')))) [2] a__U12(tt, U21(X11, X21, X3', X4')) -> s(a__length(a__U21(mark(X11), X21, X3', X4'))) [2] a__U12(tt, U22(X12, X22, X3'', X4'')) -> s(a__length(a__U22(mark(X12), X22, X3'', X4''))) [2] a__U12(tt, U23(X13, X23, X31, X41)) -> s(a__length(a__U23(mark(X13), X23, X31, X41))) [2] a__U12(tt, take(X14, X24)) -> s(a__length(a__take(mark(X14), mark(X24)))) [2] a__U12(tt, cons(X15, X25)) -> s(a__length(cons(mark(X15), X25))) [2] a__U12(tt, 0) -> s(a__length(0)) [2] a__U12(tt, tt) -> s(a__length(tt)) [2] a__U12(tt, s(X'')) -> s(a__length(s(mark(X'')))) [2] a__U12(tt, nil) -> s(a__length(nil)) [2] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(zeros, X2)) -> a__U11(a__zeros, X2) [2] mark(U11(U11(X16, X26), X2)) -> a__U11(a__U11(mark(X16), X26), X2) [2] mark(U11(U12(X17, X27), X2)) -> a__U11(a__U12(mark(X17), X27), X2) [2] mark(U11(length(X5), X2)) -> a__U11(a__length(mark(X5)), X2) [2] mark(U11(U21(X18, X28, X32, X42), X2)) -> a__U11(a__U21(mark(X18), X28, X32, X42), X2) [2] mark(U11(U22(X19, X29, X33, X43), X2)) -> a__U11(a__U22(mark(X19), X29, X33, X43), X2) [2] mark(U11(U23(X110, X210, X34, X44), X2)) -> a__U11(a__U23(mark(X110), X210, X34, X44), X2) [2] mark(U11(take(X111, X211), X2)) -> a__U11(a__take(mark(X111), mark(X211)), X2) [2] mark(U11(cons(X112, X212), X2)) -> a__U11(cons(mark(X112), X212), X2) [2] mark(U11(0, X2)) -> a__U11(0, X2) [2] mark(U11(tt, X2)) -> a__U11(tt, X2) [2] mark(U11(s(X6), X2)) -> a__U11(s(mark(X6)), X2) [2] mark(U11(nil, X2)) -> a__U11(nil, X2) [2] mark(U12(zeros, X2)) -> a__U12(a__zeros, X2) [2] mark(U12(U11(X113, X213), X2)) -> a__U12(a__U11(mark(X113), X213), X2) [2] mark(U12(U12(X114, X214), X2)) -> a__U12(a__U12(mark(X114), X214), X2) [2] mark(U12(length(X7), X2)) -> a__U12(a__length(mark(X7)), X2) [2] mark(U12(U21(X115, X215, X35, X45), X2)) -> a__U12(a__U21(mark(X115), X215, X35, X45), X2) [2] mark(U12(U22(X116, X216, X36, X46), X2)) -> a__U12(a__U22(mark(X116), X216, X36, X46), X2) [2] mark(U12(U23(X117, X217, X37, X47), X2)) -> a__U12(a__U23(mark(X117), X217, X37, X47), X2) [2] mark(U12(take(X118, X218), X2)) -> a__U12(a__take(mark(X118), mark(X218)), X2) [2] mark(U12(cons(X119, X219), X2)) -> a__U12(cons(mark(X119), X219), X2) [2] mark(U12(0, X2)) -> a__U12(0, X2) [2] mark(U12(tt, X2)) -> a__U12(tt, X2) [2] mark(U12(s(X8), X2)) -> a__U12(s(mark(X8)), X2) [2] mark(U12(nil, X2)) -> a__U12(nil, X2) [2] mark(length(zeros)) -> a__length(a__zeros) [2] mark(length(U11(X120, X220))) -> a__length(a__U11(mark(X120), X220)) [2] mark(length(U12(X121, X221))) -> a__length(a__U12(mark(X121), X221)) [2] mark(length(length(X9))) -> a__length(a__length(mark(X9))) [2] mark(length(U21(X122, X222, X38, X48))) -> a__length(a__U21(mark(X122), X222, X38, X48)) [2] mark(length(U22(X123, X223, X39, X49))) -> a__length(a__U22(mark(X123), X223, X39, X49)) [2] mark(length(U23(X124, X224, X310, X410))) -> a__length(a__U23(mark(X124), X224, X310, X410)) [2] mark(length(take(X125, X225))) -> a__length(a__take(mark(X125), mark(X225))) [2] mark(length(cons(X126, X226))) -> a__length(cons(mark(X126), X226)) [2] mark(length(0)) -> a__length(0) [2] mark(length(tt)) -> a__length(tt) [2] mark(length(s(X10))) -> a__length(s(mark(X10))) [2] mark(length(nil)) -> a__length(nil) [2] mark(U21(zeros, X2, X3, X4)) -> a__U21(a__zeros, X2, X3, X4) [2] mark(U21(U11(X127, X227), X2, X3, X4)) -> a__U21(a__U11(mark(X127), X227), X2, X3, X4) [2] mark(U21(U12(X128, X228), X2, X3, X4)) -> a__U21(a__U12(mark(X128), X228), X2, X3, X4) [2] mark(U21(length(X20), X2, X3, X4)) -> a__U21(a__length(mark(X20)), X2, X3, X4) [2] mark(U21(U21(X129, X229, X311, X411), X2, X3, X4)) -> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) [2] mark(U21(U22(X130, X230, X312, X412), X2, X3, X4)) -> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) [2] mark(U21(U23(X131, X231, X313, X413), X2, X3, X4)) -> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) [2] mark(U21(take(X132, X232), X2, X3, X4)) -> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) [2] mark(U21(cons(X133, X233), X2, X3, X4)) -> a__U21(cons(mark(X133), X233), X2, X3, X4) [2] mark(U21(0, X2, X3, X4)) -> a__U21(0, X2, X3, X4) [2] mark(U21(tt, X2, X3, X4)) -> a__U21(tt, X2, X3, X4) [2] mark(U21(s(X30), X2, X3, X4)) -> a__U21(s(mark(X30)), X2, X3, X4) [2] mark(U21(nil, X2, X3, X4)) -> a__U21(nil, X2, X3, X4) [2] mark(U22(zeros, X2, X3, X4)) -> a__U22(a__zeros, X2, X3, X4) [2] mark(U22(U11(X134, X234), X2, X3, X4)) -> a__U22(a__U11(mark(X134), X234), X2, X3, X4) [2] mark(U22(U12(X135, X235), X2, X3, X4)) -> a__U22(a__U12(mark(X135), X235), X2, X3, X4) [2] mark(U22(length(X40), X2, X3, X4)) -> a__U22(a__length(mark(X40)), X2, X3, X4) [2] mark(U22(U21(X136, X236, X314, X414), X2, X3, X4)) -> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) [2] mark(U22(U22(X137, X237, X315, X415), X2, X3, X4)) -> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) [2] mark(U22(U23(X138, X238, X316, X416), X2, X3, X4)) -> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) [2] mark(U22(take(X139, X239), X2, X3, X4)) -> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) [2] mark(U22(cons(X140, X240), X2, X3, X4)) -> a__U22(cons(mark(X140), X240), X2, X3, X4) [2] mark(U22(0, X2, X3, X4)) -> a__U22(0, X2, X3, X4) [2] mark(U22(tt, X2, X3, X4)) -> a__U22(tt, X2, X3, X4) [2] mark(U22(s(X50), X2, X3, X4)) -> a__U22(s(mark(X50)), X2, X3, X4) [2] mark(U22(nil, X2, X3, X4)) -> a__U22(nil, X2, X3, X4) [2] mark(U23(zeros, X2, X3, X4)) -> a__U23(a__zeros, X2, X3, X4) [2] mark(U23(U11(X141, X241), X2, X3, X4)) -> a__U23(a__U11(mark(X141), X241), X2, X3, X4) [2] mark(U23(U12(X142, X242), X2, X3, X4)) -> a__U23(a__U12(mark(X142), X242), X2, X3, X4) [2] mark(U23(length(X51), X2, X3, X4)) -> a__U23(a__length(mark(X51)), X2, X3, X4) [2] mark(U23(U21(X143, X243, X317, X417), X2, X3, X4)) -> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) [2] mark(U23(U22(X144, X244, X318, X418), X2, X3, X4)) -> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) [2] mark(U23(U23(X145, X245, X319, X419), X2, X3, X4)) -> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) [2] mark(U23(take(X146, X246), X2, X3, X4)) -> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) [2] mark(U23(cons(X147, X247), X2, X3, X4)) -> a__U23(cons(mark(X147), X247), X2, X3, X4) [2] mark(U23(0, X2, X3, X4)) -> a__U23(0, X2, X3, X4) [2] mark(U23(tt, X2, X3, X4)) -> a__U23(tt, X2, X3, X4) [2] mark(U23(s(X52), X2, X3, X4)) -> a__U23(s(mark(X52)), X2, X3, X4) [2] mark(U23(nil, X2, X3, X4)) -> a__U23(nil, X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 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__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 2 }-> 1 + a__length(a__zeros) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 2, X' >= 0, z' = 1 + X' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X10)) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 2 }-> a__U23(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 2 }-> a__U21(a__zeros, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 2 }-> a__U11(a__zeros, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 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__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(X'))) :|: z = 2, X' >= 0, z' = 1 + X' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X'')) :|: z = 2, z' = 1 + X'', X'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(X9))) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X10)) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__length(1 + mark(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 3 }-> a__U23(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U23(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 3 }-> a__U22(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 3 }-> a__U22(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U12(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U12(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 3 }-> a__U12(1 + 0 + 3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U11(3, X2) :|: X2 >= 0, z = 1 + 3 + X2 mark(z) -{ 2 }-> a__U11(2, X2) :|: z = 1 + 2 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__U11(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__U11(z, z') -{ 1 }-> a__U12(2, z') :|: z = 2, z' >= 0 a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__take(mark(X14), mark(X24))) :|: z = 2, z' = 1 + X14 + X24, X14 >= 0, X24 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__length(mark(z' - 1))) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U23(mark(X13), X23, X31, X41)) :|: z = 2, z' = 1 + X13 + X23 + X31 + X41, X31 >= 0, X41 >= 0, X13 >= 0, X23 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U22(mark(X12), X22, X3'', X4'')) :|: z = 2, X12 >= 0, X22 >= 0, X3'' >= 0, z' = 1 + X12 + X22 + X3'' + X4'', X4'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U21(mark(X11), X21, X3', X4')) :|: z = 2, X3' >= 0, X4' >= 0, X11 >= 0, X21 >= 0, z' = 1 + X11 + X21 + X3' + X4' a__U12(z, z') -{ 2 }-> 1 + a__length(a__U12(mark(X1''), X2'')) :|: z = 2, z' = 1 + X1'' + X2'', X1'' >= 0, X2'' >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(a__U11(mark(X1'), X2')) :|: z = 2, z' = 1 + X1' + X2', X2' >= 0, X1' >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(3) :|: z = 2, z' = 3 a__U12(z, z') -{ 2 }-> 1 + a__length(2) :|: z = 2, z' = 2 a__U12(z, z') -{ 2 }-> 1 + a__length(1) :|: z = 2, z' = 1 a__U12(z, z') -{ 2 }-> 1 + a__length(0) :|: z = 2, z' = 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(z' - 1)) :|: z = 2, z' - 1 >= 0 a__U12(z, z') -{ 2 }-> 1 + a__length(1 + mark(X15) + X25) :|: z = 2, z' = 1 + X15 + X25, X15 >= 0, X25 >= 0 a__U12(z, z') -{ 3 }-> 1 + a__length(1 + 0 + 3) :|: z = 2, z' = 3 a__U12(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, z', z'', z1) :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(z1) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 1 }-> a__U21(2, IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 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(X125), mark(X225))) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 2 }-> a__length(a__length(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__length(a__U23(mark(X124), X224, X310, X410)) :|: X124 >= 0, X410 >= 0, X224 >= 0, X310 >= 0, z = 1 + (1 + X124 + X224 + X310 + X410) mark(z) -{ 2 }-> a__length(a__U22(mark(X123), X223, X39, X49)) :|: X223 >= 0, z = 1 + (1 + X123 + X223 + X39 + X49), X49 >= 0, X39 >= 0, X123 >= 0 mark(z) -{ 2 }-> a__length(a__U21(mark(X122), X222, X38, X48)) :|: X222 >= 0, X48 >= 0, X38 >= 0, X122 >= 0, z = 1 + (1 + X122 + X222 + X38 + X48) mark(z) -{ 2 }-> a__length(a__U12(mark(X121), X221)) :|: z = 1 + (1 + X121 + X221), X221 >= 0, X121 >= 0 mark(z) -{ 2 }-> a__length(a__U11(mark(X120), X220)) :|: X120 >= 0, z = 1 + (1 + X120 + X220), X220 >= 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(X126) + X226) :|: z = 1 + (1 + X126 + X226), X126 >= 0, X226 >= 0 mark(z) -{ 3 }-> a__length(1 + 0 + 3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__U23(a__take(mark(X146), mark(X246)), X2, X3, X4) :|: X146 >= 0, z = 1 + (1 + X146 + X246) + X2 + X3 + X4, X246 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__length(mark(X51)), X2, X3, X4) :|: X51 >= 0, z = 1 + (1 + X51) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U23(mark(X145), X245, X319, X419), X2, X3, X4) :|: X319 >= 0, X245 >= 0, X145 >= 0, X419 >= 0, X3 >= 0, z = 1 + (1 + X145 + X245 + X319 + X419) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U22(mark(X144), X244, X318, X418), X2, X3, X4) :|: X244 >= 0, X418 >= 0, X144 >= 0, z = 1 + (1 + X144 + X244 + X318 + X418) + X2 + X3 + X4, X3 >= 0, X318 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(a__U21(mark(X143), X243, X317, X417), X2, X3, X4) :|: X243 >= 0, X3 >= 0, X143 >= 0, X417 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X143 + X243 + X317 + X417) + X2 + X3 + X4, X317 >= 0 mark(z) -{ 2 }-> a__U23(a__U12(mark(X142), X242), X2, X3, X4) :|: X242 >= 0, X3 >= 0, z = 1 + (1 + X142 + X242) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U23(a__U11(mark(X141), X241), X2, X3, X4) :|: z = 1 + (1 + X141 + X241) + X2 + X3 + X4, X3 >= 0, X241 >= 0, X2 >= 0, X4 >= 0, X141 >= 0 mark(z) -{ 3 }-> a__U23(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U23(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X52), X2, X3, X4) :|: X3 >= 0, z = 1 + (1 + X52) + X2 + X3 + X4, X52 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U23(1 + mark(X147) + X247, X2, X3, X4) :|: X147 >= 0, X3 >= 0, z = 1 + (1 + X147 + X247) + X2 + X3 + X4, X247 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U23(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__take(mark(X139), mark(X239)), X2, X3, X4) :|: z = 1 + (1 + X139 + X239) + X2 + X3 + X4, X3 >= 0, X239 >= 0, X2 >= 0, X4 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U22(a__length(mark(X40)), X2, X3, X4) :|: z = 1 + (1 + X40) + X2 + X3 + X4, X40 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U23(mark(X138), X238, X316, X416), X2, X3, X4) :|: z = 1 + (1 + X138 + X238 + X316 + X416) + X2 + X3 + X4, X3 >= 0, X416 >= 0, X2 >= 0, X4 >= 0, X138 >= 0, X238 >= 0, X316 >= 0 mark(z) -{ 2 }-> a__U22(a__U22(mark(X137), X237, X315, X415), X2, X3, X4) :|: X315 >= 0, z = 1 + (1 + X137 + X237 + X315 + X415) + X2 + X3 + X4, X3 >= 0, X137 >= 0, X2 >= 0, X4 >= 0, X237 >= 0, X415 >= 0 mark(z) -{ 2 }-> a__U22(a__U21(mark(X136), X236, X314, X414), X2, X3, X4) :|: X414 >= 0, X136 >= 0, X3 >= 0, X236 >= 0, X314 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X136 + X236 + X314 + X414) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(a__U12(mark(X135), X235), X2, X3, X4) :|: X135 >= 0, X3 >= 0, X235 >= 0, z = 1 + (1 + X135 + X235) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(a__U11(mark(X134), X234), X2, X3, X4) :|: X134 >= 0, X234 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X134 + X234) + X2 + X3 + X4 mark(z) -{ 3 }-> a__U22(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U22(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X50), X2, X3, X4) :|: X50 >= 0, X3 >= 0, z = 1 + (1 + X50) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U22(1 + mark(X140) + X240, X2, X3, X4) :|: X240 >= 0, z = 1 + (1 + X140 + X240) + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0, X140 >= 0 mark(z) -{ 3 }-> a__U22(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__take(mark(X132), mark(X232)), X2, X3, X4) :|: z = 1 + (1 + X132 + X232) + X2 + X3 + X4, X3 >= 0, X232 >= 0, X2 >= 0, X4 >= 0, X132 >= 0 mark(z) -{ 2 }-> a__U21(a__length(mark(X20)), X2, X3, X4) :|: z = 1 + (1 + X20) + X2 + X3 + X4, X20 >= 0, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U23(mark(X131), X231, X313, X413), X2, X3, X4) :|: X313 >= 0, X3 >= 0, X231 >= 0, X413 >= 0, z = 1 + (1 + X131 + X231 + X313 + X413) + X2 + X3 + X4, X2 >= 0, X4 >= 0, X131 >= 0 mark(z) -{ 2 }-> a__U21(a__U22(mark(X130), X230, X312, X412), X2, X3, X4) :|: z = 1 + (1 + X130 + X230 + X312 + X412) + X2 + X3 + X4, X312 >= 0, X412 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, X130 >= 0, X230 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X129), X229, X311, X411), X2, X3, X4) :|: z = 1 + (1 + X129 + X229 + X311 + X411) + X2 + X3 + X4, X311 >= 0, X411 >= 0, X229 >= 0, X3 >= 0, X129 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(X128), X228), X2, X3, X4) :|: X128 >= 0, z = 1 + (1 + X128 + X228) + X2 + X3 + X4, X3 >= 0, X228 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X127), X227), X2, X3, X4) :|: X227 >= 0, X3 >= 0, X127 >= 0, z = 1 + (1 + X127 + X227) + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(2, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 2 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1, X2, X3, X4) :|: X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + 1 + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(0, X2, X3, X4) :|: X3 >= 0, z = 1 + 0 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X30), X2, X3, X4) :|: X30 >= 0, X3 >= 0, X2 >= 0, X4 >= 0, z = 1 + (1 + X30) + X2 + X3 + X4 mark(z) -{ 2 }-> a__U21(1 + mark(X133) + X233, X2, X3, X4) :|: X233 >= 0, X3 >= 0, z = 1 + (1 + X133 + X233) + X2 + X3 + X4, X133 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 3 }-> a__U21(1 + 0 + 3, X2, X3, X4) :|: X3 >= 0, z = 1 + 3 + X2 + X3 + X4, X2 >= 0, X4 >= 0 mark(z) -{ 2 }-> a__U12(a__take(mark(X118), mark(X218)), X2) :|: X118 >= 0, z = 1 + (1 + X118 + X218) + X2, X2 >= 0, X218 >= 0 mark(z) -{ 2 }-> a__U12(a__length(mark(X7)), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U23(mark(X117), X217, X37, X47), X2) :|: X47 >= 0, X37 >= 0, X117 >= 0, X2 >= 0, z = 1 + (1 + X117 + X217 + X37 + X47) + X2, X217 >= 0 mark(z) -{ 2 }-> a__U12(a__U22(mark(X116), X216, X36, X46), X2) :|: X216 >= 0, X36 >= 0, z = 1 + (1 + X116 + X216 + X36 + X46) + X2, X116 >= 0, X46 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X115), X215, X35, X45), X2) :|: X115 >= 0, X35 >= 0, X45 >= 0, z = 1 + (1 + X115 + X215 + X35 + X45) + X2, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X114), X214), X2) :|: X114 >= 0, z = 1 + (1 + X114 + X214) + X2, X214 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X113), X213), X2) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U12(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U12(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__U12(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X8), X2) :|: z = 1 + (1 + X8) + X2, X8 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X119) + X219, X2) :|: z = 1 + (1 + X119 + X219) + X2, X219 >= 0, X2 >= 0, X119 >= 0 mark(z) -{ 3 }-> a__U12(1 + 0 + 3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U11(a__take(mark(X111), mark(X211)), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> a__U11(a__length(mark(X5)), X2) :|: X5 >= 0, z = 1 + (1 + X5) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U23(mark(X110), X210, X34, X44), X2) :|: X110 >= 0, z = 1 + (1 + X110 + X210 + X34 + X44) + X2, X2 >= 0, X210 >= 0, X34 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__U22(mark(X19), X29, X33, X43), X2) :|: X33 >= 0, X43 >= 0, X29 >= 0, X19 >= 0, z = 1 + (1 + X19 + X29 + X33 + X43) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X18), X28, X32, X42), X2) :|: X32 >= 0, X18 >= 0, X28 >= 0, z = 1 + (1 + X18 + X28 + X32 + X42) + X2, X42 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X17), X27), X2) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X16), X26), X2) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 3 }-> a__U11(3, z - 4) :|: z - 4 >= 0 mark(z) -{ 2 }-> a__U11(2, z - 3) :|: z - 3 >= 0 mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X6), X2) :|: X6 >= 0, z = 1 + (1 + X6) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X112) + X212, X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__U11(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__U11(tt, L) -> a__U12(tt, L) [1] a__U12(tt, L) -> s(a__length(mark(L))) [1] a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) [1] a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) [1] a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U11(tt, L) [1] a__take(0, IL) -> nil [1] a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X1, X2)) -> a__U12(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) [1] mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) [1] mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) [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(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X1, X2) -> U12(X1, X2) [1] a__length(X) -> length(X) [1] a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) [1] a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) [1] a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 cons :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 0 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 zeros :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 tt :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 s :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 mark :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 nil :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 a__take :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U11 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U12 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 length :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U21 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U22 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 U23 :: 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 -> 0:zeros:cons:tt:s:take:nil:U11:U12:length:U21:U22:U23 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__U11(z, z') -{ 1 }-> a__U12(2, L) :|: z = 2, L >= 0, z' = L a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U12(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'', z1) -{ 1 }-> a__U22(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U21(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U22(z, z', z'', z1) -{ 1 }-> a__U23(2, IL, M, N) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U22(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__U23(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U23(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__length(z) -{ 1 }-> a__U11(2, L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U21(2, IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, 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__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__U23(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U22(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U12(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U11(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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U11(z0, z1) -> c3 A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U12(z0, z1) -> c5 A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U21(z0, z1, z2, z3) -> c7 A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U22(z0, z1, z2, z3) -> c9 A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(nil) -> c12 A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__LENGTH(z0) -> c14 A__TAKE(0, z0) -> c15 A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) A__TAKE(z0, z1) -> c17 MARK(zeros) -> c18(A__ZEROS) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(0) -> c28 MARK(tt) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_2, A__U12_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_1, c3, c4_2, c5, c6_1, c7, c8_1, c9, c10_1, c11, c12, c13_1, c14, c15, c16_1, c17, c18_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c28, c29, c30_1, c31 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: A__TAKE(0, z0) -> c15 A__U12(z0, z1) -> c5 MARK(tt) -> c29 MARK(zeros) -> c18(A__ZEROS) MARK(nil) -> c31 A__ZEROS -> c A__TAKE(z0, z1) -> c17 A__U21(z0, z1, z2, z3) -> c7 MARK(0) -> c28 A__LENGTH(nil) -> c12 A__U11(z0, z1) -> c3 A__ZEROS -> c1 A__U23(z0, z1, z2, z3) -> c11 A__LENGTH(z0) -> c14 A__U22(z0, z1, z2, z3) -> c9 ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U12_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c2_1, c4_2, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1 ---------------------------------------- (27) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, z0) -> c4(A__LENGTH(mark(z0)), MARK(z0)) by A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2 ---------------------------------------- (29) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__U12(tt, tt) -> c4(A__LENGTH(tt), MARK(tt)) A__U12(tt, 0) -> c4(A__LENGTH(0), MARK(0)) A__U12(tt, nil) -> c4(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros), MARK(zeros)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c19(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(nil, x1)) -> c19(A__U11(nil, x1), MARK(nil)) MARK(U11(0, x1)) -> c19(A__U11(0, x1), MARK(0)) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(cons(z0, z1), x1)) -> c19(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c19(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c20_2, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1 ---------------------------------------- (39) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0, z1)) -> c20(A__U12(mark(z0), z1), MARK(z0)) by MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2 ---------------------------------------- (41) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U12(0, x1)) -> c20(A__U12(0, x1), MARK(0)) MARK(U12(nil, x1)) -> c20(A__U12(nil, x1), MARK(nil)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1), MARK(zeros)) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(cons(z0, z1), x1)) -> c20(A__U12(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1), MARK(tt)) MARK(U12(s(z0), x1)) -> c20(A__U12(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c21_2, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c21(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(0)) -> c21(A__LENGTH(0), MARK(0)) MARK(length(nil)) -> c21(A__LENGTH(nil), MARK(nil)) MARK(length(tt)) -> c21(A__LENGTH(tt), MARK(tt)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1, z2, z3)) -> c22(A__U21(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U21(0, x1, x2, x3)) -> c22(A__U21(0, x1, x2, x3), MARK(0)) MARK(U21(nil, x1, x2, x3)) -> c22(A__U21(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(A__U21(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3), MARK(tt)) MARK(U21(s(z0), x1, x2, x3)) -> c22(A__U21(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c23_2, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U22(z0, z1, z2, z3)) -> c23(A__U22(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2 ---------------------------------------- (59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U22(nil, x1, x2, x3)) -> c23(A__U22(nil, x1, x2, x3), MARK(nil)) MARK(U22(0, x1, x2, x3)) -> c23(A__U22(0, x1, x2, x3), MARK(0)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(A__U22(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3), MARK(tt)) MARK(U22(s(z0), x1, x2, x3)) -> c23(A__U22(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c24_2, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U23(z0, z1, z2, z3)) -> c24(A__U23(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U23(nil, x1, x2, x3)) -> c24(A__U23(nil, x1, x2, x3), MARK(nil)) MARK(U23(0, x1, x2, x3)) -> c24(A__U23(0, x1, x2, x3), MARK(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(A__U23(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3), MARK(tt)) MARK(U23(s(z0), x1, x2, x3)) -> c24(A__U23(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c25_2, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c25(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(nil, x1)) -> c25(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(0, x1)) -> c25(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c25(A__TAKE(tt, mark(x1)), MARK(tt)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c25(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c25(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c25(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c25(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c25(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c26_2, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c26(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(take(x0, nil)) -> c26(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, tt)) -> c26(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, 0)) -> c26(A__TAKE(mark(x0), 0), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c26(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c26(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c26(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c26(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c26(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U11(z0, z1)) -> c4(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(x0, z1)) -> c4(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U12(z0, z1)) -> c4(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) by A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(x0, z1)) -> c4(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, length(z0)) -> c4(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(x0)) -> c4(A__LENGTH(length(mark(x0))), MARK(length(x0))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0)), MARK(length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt)), MARK(length(tt))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil)), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U21(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) by A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> 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z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, 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c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) 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MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U22(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) by A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, U23(z0, z1, z2, z3)) -> c4(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) by A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), 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MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), 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x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> 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x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, take(z0, z1)) -> c4(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> 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MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), 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x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, x1)) -> c4(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), 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x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) 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c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U12(tt, zeros) -> c4(A__LENGTH(a__zeros)) by A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, 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A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> 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A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U12(tt, zeros) -> c4(A__LENGTH(zeros)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, 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x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, 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c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U11(z0, z1), x1)) -> c19(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) by MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) 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U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), 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z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(x0, z1), x2)) -> c19(A__U11(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U12(z0, z1), x1)) -> c19(A__U11(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) by MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> 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A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), 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c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(x0, z1), x2)) -> c19(A__U11(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, 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c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, 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c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(length(z0), x1)) -> c19(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, 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mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) 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mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), 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A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(x0), x1)) -> c19(A__U11(length(mark(x0)), x1), MARK(length(x0))) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1), MARK(length(0))) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1), MARK(length(tt))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, 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c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U21(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) by MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, 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c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> 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MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(A__U11(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) 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c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), 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x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U22(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) by MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, 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z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), 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c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(A__U11(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> 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c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), 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MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(U23(z0, z1, z2, z3), x1)) -> c19(A__U11(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) by MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> 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MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> 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x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(A__U11(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), 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x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(take(z0, z1), x1)) -> c19(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), 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c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) 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x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, x1), x2)) -> c19(A__U11(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), 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A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), 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MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(zeros, x1)) -> c19(A__U11(a__zeros, x1)) by MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), 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MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, 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MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, 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c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), 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z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> 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x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(zeros, x0)) -> c19(A__U11(zeros, x0)) MARK(U11(zeros, x0)) -> c19(A__U11(cons(0, zeros), x0)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> 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x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> 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U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, 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c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), 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MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, 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c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U11(z0, z1), x1)) -> c20(A__U12(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) by MARK(U12(U11(x0, z1), x2)) -> c20(A__U12(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, 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c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, 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x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, 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x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(x0, z1), x2)) -> c20(A__U12(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, 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x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, 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c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> 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MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, 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MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(x0, z1), x2)) -> c20(A__U12(U11(mark(x0), z1), x2), MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2), MARK(U11(zeros, x1))) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2), MARK(U11(0, x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, 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A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) 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z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), 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U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U12(z0, z1), x1)) -> c20(A__U12(a__U12(mark(z0), z1), x1), MARK(U12(z0, z1))) by MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) 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A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), 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take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(x0, z1), x2)) -> c20(A__U12(U12(mark(x0), z1), x2), MARK(U12(x0, z1))) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2), MARK(U12(0, x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), 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MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> 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MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, 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x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(length(z0), x1)) -> c20(A__U12(a__length(mark(z0)), x1), MARK(length(z0))) by MARK(U12(length(x0), x1)) -> c20(A__U12(length(mark(x0)), x1), MARK(length(x0))) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> 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MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(x0), x1)) -> c20(A__U12(length(mark(x0)), x1), MARK(length(x0))) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, 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MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), 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c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1), MARK(length(0))) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1), MARK(length(tt))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) 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mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> 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MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U21(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U21(mark(z0), z1, z2, z3), x1), MARK(U21(z0, z1, z2, z3))) by MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, 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MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> 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MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(A__U12(U21(mark(x0), z1, z2, z3), x4), MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4), MARK(U21(0, x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, 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c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U22(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U22(mark(z0), z1, z2, z3), x1), MARK(U22(z0, z1, z2, z3))) by MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, 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U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, take(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U11(take(x0, cons(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U11(take(x0, 0), x2)) -> c19(A__U11(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U11(take(x0, tt), x2)) -> c19(A__U11(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), 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c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), 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x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(A__U12(U22(mark(x0), z1, z2, z3), x4), MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4), MARK(U22(0, x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), 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c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, 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x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(U23(z0, z1, z2, z3), x1)) -> c20(A__U12(a__U23(mark(z0), z1, z2, z3), x1), MARK(U23(z0, z1, z2, z3))) by MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), 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x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) 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MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> 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MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, 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MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(A__U12(U23(mark(x0), z1, z2, z3), x4), MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4), MARK(U23(0, x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, 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-> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), 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c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) 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c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), 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z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), 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MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(take(z0, z1), x1)) -> c20(A__U12(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) by MARK(U12(take(x0, x1), x2)) -> c20(A__U12(take(mark(x0), mark(x1)), x2), MARK(take(x0, x1))) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> 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c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), 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MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), 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MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> 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x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> 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MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(zeros, x1)) -> c20(A__U12(a__zeros, x1)) by MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, 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z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, 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c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2), MARK(U12(zeros, x1))) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, 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x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U12(zeros, x0)) -> c20(A__U12(zeros, x0)) MARK(U12(zeros, x0)) -> c20(A__U12(cons(0, zeros), x0)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) 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MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, 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c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) 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-> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), 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z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, 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MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> 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MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) 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length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), 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MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U11(z0, z1))) -> c21(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), 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tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> 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c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, 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MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U12(U21(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U12(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) 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MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> 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c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(x0, z1))) -> c21(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, 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MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> 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MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, 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z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U12(z0, z1))) -> c21(A__LENGTH(a__U12(mark(z0), z1)), MARK(U12(z0, z1))) by MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), 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MARK(U12(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), 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-> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, 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MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(x0, z1))) -> c21(A__LENGTH(U12(mark(x0), z1)), MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1)), MARK(U12(zeros, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1)), MARK(U12(0, x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1)), MARK(U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> 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x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, 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MARK(U12(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U21(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U12(U21(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(length(z0))) -> c21(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) by MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, 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MARK(U12(length(U23(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U12(length(take(z0, z1)), x1)) -> c20(A__U12(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U12(length(cons(z0, z1)), x1)) -> c20(A__U12(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U12(length(s(z0)), x1)) -> c20(A__U12(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U12(length(x0), x1)) -> c20(MARK(length(x0))) MARK(U12(length(0), x1)) -> c20(A__U12(a__length(0), x1)) MARK(U12(length(tt), x1)) -> c20(A__U12(a__length(tt), x1)) MARK(U12(length(nil), x1)) -> c20(A__U12(a__length(nil), x1)) MARK(U12(U21(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U12(U21(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U12(U21(U12(z0, z1), x1, x2, x3), x4)) 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MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), 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c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, 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c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U12(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(x0))) -> c21(A__LENGTH(length(mark(x0))), MARK(length(x0))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0)), MARK(length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt)), MARK(length(tt))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil)), MARK(length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), 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MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, 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U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), 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x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U22(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U12(U22(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U12(U22(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U12(U22(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U12(U22(x0, z1, z2, z3), x4)) -> c20(MARK(U22(x0, z1, z2, z3))) MARK(U12(U22(0, x1, x2, x3), x4)) -> c20(A__U12(a__U22(0, x1, x2, x3), x4)) MARK(U12(U22(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U22(nil, x1, x2, x3), x4)) MARK(U12(U23(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U12(U23(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U12(U23(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U12(U23(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U12(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U12(U23(take(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U12(U23(cons(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U12(U23(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U12(U23(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U12(U23(x0, z1, z2, z3), x4)) -> c20(MARK(U23(x0, z1, z2, z3))) MARK(U12(U23(0, x1, x2, x3), x4)) -> c20(A__U12(a__U23(0, x1, x2, x3), x4)) MARK(U12(U23(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U23(nil, x1, x2, x3), x4)) MARK(U12(take(x0, zeros), x2)) -> c20(A__U12(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U12(take(x0, U11(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U21(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) by MARK(length(U21(x0, z1, z2, z3))) -> c21(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> 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A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) 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MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(x0, z1, z2, z3))) -> c21(A__LENGTH(U21(mark(x0), z1, z2, z3)), MARK(U21(x0, z1, z2, z3))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3)), MARK(U21(0, x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3)), MARK(U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_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__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, 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x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, 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MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U12(U21(tt, x1, x2, x3), x4)) -> c20(A__U12(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U12(U21(s(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U12(U21(x0, z1, z2, z3), x4)) -> c20(MARK(U21(x0, z1, z2, z3))) MARK(U12(U21(0, x1, x2, x3), x4)) -> c20(A__U12(a__U21(0, x1, x2, x3), x4)) MARK(U12(U21(nil, x1, x2, x3), x4)) -> c20(A__U12(a__U21(nil, x1, x2, x3), x4)) MARK(U12(U22(zeros, x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U12(U22(U11(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U12(U22(U12(z0, z1), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U12(U22(length(z0), x1, x2, x3), x4)) -> c20(A__U12(a__U22(a__length(mark(z0)), x1, x2, x3), x4), 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x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U22(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) by MARK(length(U22(x0, z1, z2, z3))) -> c21(A__LENGTH(U22(mark(x0), z1, z2, z3)), MARK(U22(x0, z1, z2, z3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) 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x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, 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x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, length(z0)), x2)) -> c19(A__U11(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U11(take(x0, U21(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U11(take(x0, U22(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U11(take(x0, U23(z0, z1, z2, z3)), x2)) -> c19(A__U11(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U11(take(x0, 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x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> 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MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, 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MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), 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MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), 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MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3)), MARK(U22(0, x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3)), MARK(U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, 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MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> 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c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), 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a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U12(take(x0, U12(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U12(take(x0, length(z0)), x2)) -> c20(A__U12(a__take(mark(x0), a__length(mark(z0))), x2), MARK(take(x0, length(z0)))) MARK(U12(take(x0, U21(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(U12(take(x0, U22(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(U12(take(x0, U23(z0, z1, z2, z3)), x2)) -> c20(A__U12(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3)), x2), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(U12(take(x0, take(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), a__take(mark(z0), mark(z1))), x2), MARK(take(x0, take(z0, z1)))) MARK(U12(take(x0, cons(z0, z1)), x2)) -> c20(A__U12(a__take(mark(x0), cons(mark(z0), z1)), x2), MARK(take(x0, cons(z0, z1)))) MARK(U12(take(x0, 0), x2)) -> c20(A__U12(a__take(mark(x0), 0), x2), MARK(take(x0, 0))) MARK(U12(take(x0, tt), x2)) -> c20(A__U12(a__take(mark(x0), tt), x2), MARK(take(x0, tt))) MARK(U12(take(x0, s(z0)), x2)) -> c20(A__U12(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U12(take(x0, nil), x2)) -> c20(A__U12(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U12(take(zeros, x1), x2)) -> c20(A__U12(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U12(take(U11(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U12(take(U12(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U12(take(length(z0), x1), x2)) -> c20(A__U12(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U12(take(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U12(take(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U12(take(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U12(take(take(z0, z1), x1), x2)) -> c20(A__U12(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U12(take(cons(z0, z1), x1), x2)) -> c20(A__U12(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U12(take(0, x1), x2)) -> c20(A__U12(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U12(take(tt, x1), x2)) -> c20(A__U12(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U12(take(s(z0), x1), x2)) -> c20(A__U12(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U12(take(nil, x1), x2)) -> c20(A__U12(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U12(take(x0, x1), x2)) -> c20(MARK(take(x0, x1))) A__U12(tt, U12(zeros, x1)) -> c4(A__LENGTH(a__U12(a__zeros, x1))) MARK(U11(U12(zeros, x1), x2)) -> c19(A__U11(a__U12(a__zeros, x1), x2)) MARK(U12(U12(zeros, x1), x2)) -> c20(A__U12(a__U12(a__zeros, x1), x2)) MARK(length(U11(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) MARK(length(U11(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) MARK(length(U11(length(z0), x1))) -> c21(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) MARK(length(U11(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(length(U11(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(length(U11(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(length(U11(take(z0, z1), x1))) -> c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), 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MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) 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c21(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) MARK(length(U11(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) MARK(length(U11(tt, x1))) -> c21(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) MARK(length(U11(s(z0), x1))) -> c21(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) MARK(length(U11(x0, z1))) -> c21(MARK(U11(x0, z1))) MARK(length(U11(zeros, x1))) -> c21(A__LENGTH(a__U11(a__zeros, x1))) MARK(length(U11(0, x1))) -> c21(A__LENGTH(a__U11(0, x1))) MARK(length(U11(nil, x1))) -> c21(A__LENGTH(a__U11(nil, x1))) MARK(length(U12(U11(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) MARK(length(U12(U12(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) MARK(length(U12(length(z0), x1))) -> c21(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) MARK(length(U12(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(length(U12(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(length(U12(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(length(U12(take(z0, z1), x1))) -> c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(U23(z0, z1, z2, z3))) -> c21(A__LENGTH(a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) by MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) 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MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, 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z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), 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c21(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) MARK(length(U12(cons(z0, z1), x1))) -> c21(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) MARK(length(U12(tt, x1))) -> c21(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) MARK(length(U12(s(z0), x1))) -> c21(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) MARK(length(U12(x0, z1))) -> c21(MARK(U12(x0, z1))) MARK(length(U12(zeros, x1))) -> c21(A__LENGTH(a__U12(a__zeros, x1))) MARK(length(U12(0, x1))) -> c21(A__LENGTH(a__U12(0, x1))) MARK(length(U12(nil, x1))) -> c21(A__LENGTH(a__U12(nil, x1))) MARK(length(length(zeros))) -> c21(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) MARK(length(length(U11(z0, z1)))) -> c21(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) MARK(length(length(U12(z0, z1)))) -> c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> 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c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, 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MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), 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MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), 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mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U12(U11(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U12(U11(length(z0), x1), x2)) -> c20(A__U12(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U12(U11(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U12(U11(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U12(U11(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U12(U11(take(z0, z1), x1), x2)) -> c20(A__U12(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U12(U11(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U12(U11(tt, x1), x2)) -> c20(A__U12(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U12(U11(s(z0), x1), x2)) -> c20(A__U12(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U12(U11(x0, z1), x2)) -> c20(MARK(U11(x0, z1))) MARK(U12(U11(zeros, x1), x2)) -> c20(A__U12(a__U11(a__zeros, x1), x2)) MARK(U12(U11(0, x1), x2)) -> c20(A__U12(a__U11(0, x1), x2)) MARK(U12(U11(nil, x1), x2)) -> c20(A__U12(a__U11(nil, x1), x2)) MARK(U12(U12(U11(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U12(U12(U12(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U12(U12(length(z0), x1), x2)) -> c20(A__U12(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U12(U12(U21(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U12(U12(U22(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U12(U12(U23(z0, z1, z2, z3), x1), x2)) -> c20(A__U12(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U12(U12(take(z0, z1), x1), x2)) -> c20(A__U12(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U12(U12(cons(z0, z1), x1), x2)) -> c20(A__U12(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U12(U12(tt, x1), x2)) -> c20(A__U12(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U12(U12(s(z0), x1), x2)) -> c20(A__U12(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U12(U12(x0, z1), x2)) -> c20(MARK(U12(x0, z1))) MARK(U12(U12(0, x1), x2)) -> c20(A__U12(a__U12(0, x1), x2)) MARK(U12(U12(nil, x1), x2)) -> c20(A__U12(a__U12(nil, x1), x2)) MARK(U12(length(zeros), x1)) -> c20(A__U12(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U12(length(U11(z0, z1)), x1)) -> c20(A__U12(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U12(length(U12(z0, z1)), x1)) -> c20(A__U12(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U12(length(length(z0)), x1)) -> c20(A__U12(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U12(length(U21(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U12(length(U22(z0, z1, z2, z3)), x1)) -> c20(A__U12(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) 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c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(A__LENGTH(U23(mark(x0), z1, z2, z3)), MARK(U23(x0, z1, z2, z3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3)), MARK(U23(0, x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3)), MARK(U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> 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MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) 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x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> 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c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(take(z0, z1))) -> c21(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(length(take(x0, x1))) -> c21(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), 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MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> 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MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), 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MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) 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MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), 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MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, 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MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> 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c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, x1))) -> c21(A__LENGTH(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> 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c21(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) MARK(length(length(length(z0)))) -> c21(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) MARK(length(length(U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) MARK(length(length(U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) MARK(length(length(U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) MARK(length(length(take(z0, z1)))) -> c21(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) MARK(length(length(cons(z0, z1)))) -> c21(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) MARK(length(length(s(z0)))) -> c21(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) MARK(length(length(x0))) -> c21(MARK(length(x0))) MARK(length(length(0))) -> c21(A__LENGTH(a__length(0))) MARK(length(length(tt))) -> c21(A__LENGTH(a__length(tt))) MARK(length(length(nil))) -> c21(A__LENGTH(a__length(nil))) MARK(length(U21(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) MARK(length(U21(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(length(U21(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(length(U21(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) MARK(length(U21(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U21(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(length(U21(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(length(U21(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) MARK(length(U21(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) MARK(length(U21(x0, z1, z2, z3))) -> c21(MARK(U21(x0, z1, z2, z3))) MARK(length(U21(0, x1, x2, x3))) -> c21(A__LENGTH(a__U21(0, x1, x2, x3))) MARK(length(U21(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U21(nil, x1, x2, x3))) MARK(length(U22(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) MARK(length(U22(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(length(U22(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(zeros)) -> c21(A__LENGTH(a__zeros)) by MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, 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U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> 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c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U21(U11(z0, z1), x1, x2, x3))) A__U12(tt, U21(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U21(U12(z0, z1), x1, x2, x3))) A__U12(tt, U21(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__length(mark(z0)), x1, x2, x3)), MARK(U21(length(z0), x1, x2, x3))) A__U12(tt, U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U21(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U21(take(z0, z1), x1, x2, x3))) A__U12(tt, U21(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U21(cons(mark(z0), z1), x1, x2, x3)), MARK(U21(cons(z0, z1), x1, x2, x3))) A__U12(tt, U21(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U21(tt, x1, x2, x3)), MARK(U21(tt, x1, x2, x3))) A__U12(tt, U21(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U21(s(mark(z0)), x1, x2, x3)), MARK(U21(s(z0), x1, x2, x3))) A__U12(tt, U21(x0, z1, z2, z3)) -> c4(MARK(U21(x0, z1, z2, z3))) A__U12(tt, U21(0, x1, x2, x3)) -> c4(A__LENGTH(a__U21(0, x1, x2, x3))) A__U12(tt, U21(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U21(nil, x1, x2, x3))) A__U12(tt, U22(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__zeros, x1, x2, x3)), MARK(U22(zeros, x1, x2, x3))) A__U12(tt, U22(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U22(U11(z0, z1), x1, x2, x3))) A__U12(tt, U22(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U22(U12(z0, z1), x1, x2, x3))) A__U12(tt, U22(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) A__U12(tt, U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U22(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) A__U12(tt, U22(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) A__U12(tt, U22(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) A__U12(tt, U22(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) A__U12(tt, U22(x0, z1, z2, z3)) -> c4(MARK(U22(x0, z1, z2, z3))) A__U12(tt, U22(0, x1, x2, x3)) -> c4(A__LENGTH(a__U22(0, x1, x2, x3))) A__U12(tt, U22(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U22(nil, x1, x2, x3))) A__U12(tt, U23(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) A__U12(tt, U23(U11(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) A__U12(tt, U23(U12(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) A__U12(tt, U23(length(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) A__U12(tt, U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) A__U12(tt, U23(take(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) A__U12(tt, U23(cons(z0, z1), x1, x2, x3)) -> c4(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) A__U12(tt, U23(tt, x1, x2, x3)) -> c4(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) A__U12(tt, U23(s(z0), x1, x2, x3)) -> c4(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) A__U12(tt, U23(x0, z1, z2, z3)) -> c4(MARK(U23(x0, z1, z2, z3))) A__U12(tt, U23(0, x1, x2, x3)) -> c4(A__LENGTH(a__U23(0, x1, x2, x3))) A__U12(tt, U23(nil, x1, x2, x3)) -> c4(A__LENGTH(a__U23(nil, x1, x2, x3))) A__U12(tt, take(x0, zeros)) -> c4(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) A__U12(tt, take(x0, U11(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) A__U12(tt, take(x0, U12(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) A__U12(tt, take(x0, length(z0))) -> c4(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) A__U12(tt, take(x0, U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) A__U12(tt, take(x0, U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) A__U12(tt, take(x0, U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) A__U12(tt, take(x0, take(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) A__U12(tt, take(x0, cons(z0, z1))) -> c4(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) A__U12(tt, take(x0, 0)) -> c4(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) A__U12(tt, take(x0, tt)) -> c4(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) A__U12(tt, take(x0, s(z0))) -> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), 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length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(length(zeros)) -> c21(A__LENGTH(zeros)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(length(zeros)) -> c21(A__LENGTH(zeros)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, 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x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, 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0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(U11(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) by MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, 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c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), 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z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> 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-> c4(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) A__U12(tt, take(x0, nil)) -> c4(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) A__U12(tt, take(zeros, x1)) -> c4(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) A__U12(tt, take(U11(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) A__U12(tt, take(U12(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) A__U12(tt, take(length(z0), x1)) -> c4(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) A__U12(tt, take(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) A__U12(tt, take(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) A__U12(tt, take(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) A__U12(tt, take(take(z0, z1), x1)) -> c4(A__LENGTH(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) A__U12(tt, take(cons(z0, z1), x1)) -> c4(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) A__U12(tt, take(0, x1)) -> c4(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) A__U12(tt, take(tt, x1)) -> c4(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) A__U12(tt, take(s(z0), x1)) -> c4(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) A__U12(tt, take(nil, x1)) -> c4(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) A__U12(tt, take(x0, x1)) -> c4(MARK(take(x0, x1))) A__U12(tt, zeros) -> c4(A__LENGTH(cons(0, zeros))) MARK(U11(U11(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U11(mark(z0), z1), x1), x2), MARK(U11(U11(z0, z1), x1))) MARK(U11(U11(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__U12(mark(z0), z1), x1), x2), MARK(U11(U12(z0, z1), x1))) MARK(U11(U11(length(z0), x1), x2)) -> c19(A__U11(a__U11(a__length(mark(z0)), x1), x2), MARK(U11(length(z0), x1))) MARK(U11(U11(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U11(U11(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U11(U11(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U11(U11(take(z0, z1), x1), x2)) -> c19(A__U11(a__U11(a__take(mark(z0), mark(z1)), x1), x2), MARK(U11(take(z0, z1), x1))) MARK(U11(U11(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U11(cons(mark(z0), z1), x1), x2), MARK(U11(cons(z0, z1), x1))) MARK(U11(U11(tt, x1), x2)) -> c19(A__U11(a__U11(tt, x1), x2), MARK(U11(tt, x1))) MARK(U11(U11(s(z0), x1), x2)) -> c19(A__U11(a__U11(s(mark(z0)), x1), x2), MARK(U11(s(z0), x1))) MARK(U11(U11(x0, z1), x2)) -> c19(MARK(U11(x0, z1))) MARK(U11(U11(0, x1), x2)) -> c19(A__U11(a__U11(0, x1), x2)) MARK(U11(U11(nil, x1), x2)) -> c19(A__U11(a__U11(nil, x1), x2)) MARK(U11(U12(U11(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U11(mark(z0), z1), x1), x2), MARK(U12(U11(z0, z1), x1))) MARK(U11(U12(U12(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__U12(mark(z0), z1), x1), x2), MARK(U12(U12(z0, z1), x1))) MARK(U11(U12(length(z0), x1), x2)) -> c19(A__U11(a__U12(a__length(mark(z0)), x1), x2), MARK(U12(length(z0), x1))) MARK(U11(U12(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U21(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U21(z0, z1, z2, z3), x1))) MARK(U11(U12(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U22(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U22(z0, z1, z2, z3), x1))) MARK(U11(U12(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__U12(a__U23(mark(z0), z1, z2, z3), x1), x2), MARK(U12(U23(z0, z1, z2, z3), x1))) MARK(U11(U12(take(z0, z1), x1), x2)) -> c19(A__U11(a__U12(a__take(mark(z0), mark(z1)), x1), x2), MARK(U12(take(z0, z1), x1))) MARK(U11(U12(cons(z0, z1), x1), x2)) -> c19(A__U11(a__U12(cons(mark(z0), z1), x1), x2), MARK(U12(cons(z0, z1), x1))) MARK(U11(U12(tt, x1), x2)) -> c19(A__U11(a__U12(tt, x1), x2), MARK(U12(tt, x1))) MARK(U11(U12(s(z0), x1), x2)) -> c19(A__U11(a__U12(s(mark(z0)), x1), x2), MARK(U12(s(z0), x1))) MARK(U11(U12(x0, z1), x2)) -> c19(MARK(U12(x0, z1))) MARK(U11(U12(0, x1), x2)) -> c19(A__U11(a__U12(0, x1), x2)) MARK(U11(U12(nil, x1), x2)) -> c19(A__U11(a__U12(nil, x1), x2)) MARK(U11(length(zeros), x1)) -> c19(A__U11(a__length(a__zeros), x1), MARK(length(zeros))) MARK(U11(length(U11(z0, z1)), x1)) -> c19(A__U11(a__length(a__U11(mark(z0), z1)), x1), MARK(length(U11(z0, z1)))) MARK(U11(length(U12(z0, z1)), x1)) -> c19(A__U11(a__length(a__U12(mark(z0), z1)), x1), MARK(length(U12(z0, z1)))) MARK(U11(length(length(z0)), x1)) -> c19(A__U11(a__length(a__length(mark(z0))), x1), MARK(length(length(z0)))) MARK(U11(length(U21(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U21(mark(z0), z1, z2, z3)), x1), MARK(length(U21(z0, z1, z2, z3)))) MARK(U11(length(U22(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U22(mark(z0), z1, z2, z3)), x1), MARK(length(U22(z0, z1, z2, z3)))) MARK(U11(length(U23(z0, z1, z2, z3)), x1)) -> c19(A__U11(a__length(a__U23(mark(z0), z1, z2, z3)), x1), MARK(length(U23(z0, z1, z2, z3)))) MARK(U11(length(take(z0, z1)), x1)) -> c19(A__U11(a__length(a__take(mark(z0), mark(z1))), x1), MARK(length(take(z0, z1)))) MARK(U11(length(cons(z0, z1)), x1)) -> c19(A__U11(a__length(cons(mark(z0), z1)), x1), MARK(length(cons(z0, z1)))) MARK(U11(length(s(z0)), x1)) -> c19(A__U11(a__length(s(mark(z0))), x1), MARK(length(s(z0)))) MARK(U11(length(x0), x1)) -> c19(MARK(length(x0))) MARK(U11(length(0), x1)) -> c19(A__U11(a__length(0), x1)) MARK(U11(length(tt), x1)) -> c19(A__U11(a__length(tt), x1)) MARK(U11(length(nil), x1)) -> c19(A__U11(a__length(nil), x1)) MARK(U11(U21(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__zeros, x1, x2, x3), x4), MARK(U21(zeros, x1, x2, x3))) MARK(U11(U21(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U11(z0, z1), x1, x2, x3))) MARK(U11(U21(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U21(U12(z0, z1), x1, x2, x3))) MARK(U11(U21(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__length(mark(z0)), x1, x2, x3), x4), MARK(U21(length(z0), x1, x2, x3))) MARK(U11(U21(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), 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MARK(length(U22(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__length(mark(z0)), x1, x2, x3)), MARK(U22(length(z0), x1, x2, x3))) MARK(length(U22(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U22(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(length(U22(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U22(cons(mark(z0), z1), x1, x2, x3)), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(length(U22(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U22(tt, x1, x2, x3)), MARK(U22(tt, x1, x2, x3))) MARK(length(U22(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U22(s(mark(z0)), x1, x2, x3)), MARK(U22(s(z0), x1, x2, x3))) MARK(length(U22(x0, z1, z2, z3))) -> c21(MARK(U22(x0, z1, z2, z3))) MARK(length(U22(0, x1, x2, x3))) -> c21(A__LENGTH(a__U22(0, x1, x2, x3))) MARK(length(U22(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U22(nil, x1, x2, x3))) MARK(length(U23(zeros, x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__zeros, x1, x2, x3)), MARK(U23(zeros, x1, x2, x3))) MARK(length(U23(U11(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U11(mark(z0), z1), x1, x2, x3)), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(length(U23(U12(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U12(mark(z0), z1), x1, x2, x3)), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(length(U23(length(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__length(mark(z0)), x1, x2, x3)), MARK(U23(length(z0), x1, x2, x3))) MARK(length(U23(U21(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U22(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(U23(z0, z1, z2, z3), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3)), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(length(U23(take(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3)), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(length(U23(cons(z0, z1), x1, x2, x3))) -> c21(A__LENGTH(a__U23(cons(mark(z0), z1), x1, x2, x3)), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(length(U23(tt, x1, x2, x3))) -> c21(A__LENGTH(a__U23(tt, x1, x2, x3)), MARK(U23(tt, x1, x2, x3))) MARK(length(U23(s(z0), x1, x2, x3))) -> c21(A__LENGTH(a__U23(s(mark(z0)), x1, x2, x3)), MARK(U23(s(z0), x1, x2, x3))) MARK(length(U23(x0, z1, z2, z3))) -> c21(MARK(U23(x0, z1, z2, z3))) MARK(length(U23(0, x1, x2, x3))) -> c21(A__LENGTH(a__U23(0, x1, x2, x3))) MARK(length(U23(nil, x1, x2, x3))) -> c21(A__LENGTH(a__U23(nil, x1, x2, x3))) MARK(length(take(x0, zeros))) -> c21(A__LENGTH(a__take(mark(x0), a__zeros)), MARK(take(x0, zeros))) MARK(length(take(x0, U11(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U11(mark(z0), z1))), MARK(take(x0, U11(z0, z1)))) MARK(length(take(x0, U12(z0, z1)))) -> c21(A__LENGTH(a__take(mark(x0), a__U12(mark(z0), z1))), MARK(take(x0, U12(z0, z1)))) MARK(length(take(x0, length(z0)))) -> c21(A__LENGTH(a__take(mark(x0), a__length(mark(z0)))), MARK(take(x0, length(z0)))) MARK(length(take(x0, U21(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U21(mark(z0), z1, z2, z3))), MARK(take(x0, U21(z0, z1, z2, z3)))) MARK(length(take(x0, U22(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U22(mark(z0), z1, z2, z3))), MARK(take(x0, U22(z0, z1, z2, z3)))) MARK(length(take(x0, U23(z0, z1, z2, z3)))) -> c21(A__LENGTH(a__take(mark(x0), a__U23(mark(z0), z1, z2, z3))), MARK(take(x0, U23(z0, z1, z2, z3)))) MARK(length(take(x0, take(z0, z1)))) -> c21(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)))) -> c21(A__LENGTH(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(length(take(x0, 0))) -> c21(A__LENGTH(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(length(take(x0, tt))) -> c21(A__LENGTH(a__take(mark(x0), tt)), MARK(take(x0, tt))) MARK(length(take(x0, s(z0)))) -> c21(A__LENGTH(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(length(take(x0, nil))) -> c21(A__LENGTH(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(length(take(zeros, x1))) -> c21(A__LENGTH(a__take(a__zeros, mark(x1))), MARK(take(zeros, x1))) MARK(length(take(U11(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U11(mark(z0), z1), mark(x1))), MARK(take(U11(z0, z1), x1))) MARK(length(take(U12(z0, z1), x1))) -> c21(A__LENGTH(a__take(a__U12(mark(z0), z1), mark(x1))), MARK(take(U12(z0, z1), x1))) MARK(length(take(length(z0), x1))) -> c21(A__LENGTH(a__take(a__length(mark(z0)), mark(x1))), MARK(take(length(z0), x1))) MARK(length(take(U21(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(length(take(U22(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(length(take(U23(z0, z1, z2, z3), x1))) -> c21(A__LENGTH(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1))), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(length(take(take(z0, z1), x1))) -> c21(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))) -> c21(A__LENGTH(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(length(take(0, x1))) -> c21(A__LENGTH(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(length(take(tt, x1))) -> c21(A__LENGTH(a__take(tt, mark(x1))), MARK(take(tt, x1))) MARK(length(take(s(z0), x1))) -> c21(A__LENGTH(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(length(take(nil, x1))) -> c21(A__LENGTH(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(length(take(x0, x1))) -> c21(MARK(take(x0, x1))) MARK(length(zeros)) -> c21(A__LENGTH(cons(0, zeros))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(A__U21(U11(mark(x0), z1), x2, x3, x4), MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4), MARK(U11(zeros, x1))) MARK(U21(U11(U11(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U11(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U11(z0, z1), x1))) MARK(U21(U11(U12(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U12(mark(z0), z1), x1), x2, x3, x4), MARK(U11(U12(z0, z1), x1))) MARK(U21(U11(length(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__length(mark(z0)), x1), x2, x3, x4), MARK(U11(length(z0), x1))) MARK(U21(U11(U21(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4), MARK(U11(0, x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(tt, z0) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt, z0) -> s(a__length(mark(z0))) a__U12(z0, z1) -> U12(z0, z1) a__U21(tt, z0, z1, z2) -> a__U22(tt, z0, z1, z2) a__U21(z0, z1, z2, z3) -> U21(z0, z1, z2, z3) a__U22(tt, z0, z1, z2) -> a__U23(tt, z0, z1, z2) a__U22(z0, z1, z2, z3) -> U22(z0, z1, z2, z3) a__U23(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U23(z0, z1, z2, z3) -> U23(z0, z1, z2, z3) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U11(tt, z1) a__length(z0) -> length(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> a__U21(tt, z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0, z1)) -> a__U12(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U21(z0, z1, z2, z3)) -> a__U21(mark(z0), z1, z2, z3) mark(U22(z0, z1, z2, z3)) -> a__U22(mark(z0), z1, z2, z3) mark(U23(z0, z1, z2, z3)) -> a__U23(mark(z0), z1, z2, z3) 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(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> 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c22(A__U21(a__U11(a__U21(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U21(z0, z1, z2, z3), x1))) MARK(U21(U11(U22(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U22(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U22(z0, z1, z2, z3), x1))) MARK(U21(U11(U23(z0, z1, z2, z3), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__U23(mark(z0), z1, z2, z3), x1), x2, x3, x4), MARK(U11(U23(z0, z1, z2, z3), x1))) MARK(U21(U11(take(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__take(mark(z0), mark(z1)), x1), x2, x3, x4), MARK(U11(take(z0, z1), x1))) MARK(U21(U11(cons(z0, z1), x1), x2, x3, x4)) -> c22(A__U21(a__U11(cons(mark(z0), z1), x1), x2, x3, x4), MARK(U11(cons(z0, z1), x1))) MARK(U21(U11(tt, x1), x2, x3, x4)) -> c22(A__U21(a__U11(tt, x1), x2, x3, x4), MARK(U11(tt, x1))) MARK(U21(U11(s(z0), x1), x2, x3, x4)) -> c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4)) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4)) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4)) S tuples: A__U11(tt, z0) -> c2(A__U12(tt, z0)) A__U21(tt, z0, z1, z2) -> c6(A__U22(tt, z0, z1, z2)) A__U22(tt, z0, z1, z2) -> c8(A__U23(tt, z0, z1, z2)) A__U23(tt, z0, z1, z2) -> c10(MARK(z2)) A__LENGTH(cons(z0, z1)) -> c13(A__U11(tt, z1)) A__TAKE(s(z0), cons(z1, z2)) -> c16(A__U21(tt, z2, z0, z1)) MARK(cons(z0, z1)) -> c27(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) A__U12(tt, cons(z0, z1)) -> c4(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U12(tt, s(z0)) -> c4(MARK(s(z0))) MARK(U11(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c19(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c19(MARK(s(z0))) MARK(U12(cons(z0, z1), x1)) -> c20(MARK(cons(z0, z1))) MARK(U12(tt, x1)) -> c20(A__U12(tt, x1)) MARK(U12(s(z0), x1)) -> c20(MARK(s(z0))) MARK(length(cons(z0, z1))) -> c21(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c21(MARK(s(z0))) MARK(U21(U12(z0, z1), x1, x2, x3)) -> c22(A__U21(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U21(length(z0), x1, x2, x3)) -> c22(A__U21(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U21(U21(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3)) -> c22(A__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1, x2, x3)) -> c22(A__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U21(zeros, x1, x2, x3)) -> c22(A__U21(a__zeros, x1, x2, x3)) MARK(U21(cons(z0, z1), x1, x2, x3)) -> c22(MARK(cons(z0, z1))) MARK(U21(tt, x1, x2, x3)) -> c22(A__U21(tt, x1, x2, x3)) MARK(U21(s(z0), x1, x2, x3)) -> c22(MARK(s(z0))) MARK(U22(U11(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U22(U12(z0, z1), x1, x2, x3)) -> c23(A__U22(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U22(length(z0), x1, x2, x3)) -> c23(A__U22(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3)) -> c23(A__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U22(take(z0, z1), x1, x2, x3)) -> c23(A__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U22(zeros, x1, x2, x3)) -> c23(A__U22(a__zeros, x1, x2, x3)) MARK(U22(cons(z0, z1), x1, x2, x3)) -> c23(MARK(cons(z0, z1))) MARK(U22(tt, x1, x2, x3)) -> c23(A__U22(tt, x1, x2, x3)) MARK(U22(s(z0), x1, x2, x3)) -> c23(MARK(s(z0))) MARK(U23(U11(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U23(U12(z0, z1), x1, x2, x3)) -> c24(A__U23(a__U12(mark(z0), z1), x1, x2, x3), MARK(U12(z0, z1))) MARK(U23(length(z0), x1, x2, x3)) -> c24(A__U23(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U21(z0, z1, z2, z3))) MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U22(z0, z1, z2, z3))) MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3)) -> c24(A__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U23(z0, z1, z2, z3))) MARK(U23(take(z0, z1), x1, x2, x3)) -> c24(A__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U23(zeros, x1, x2, x3)) -> c24(A__U23(a__zeros, x1, x2, x3)) MARK(U23(cons(z0, z1), x1, x2, x3)) -> c24(MARK(cons(z0, z1))) MARK(U23(tt, x1, x2, x3)) -> c24(A__U23(tt, x1, x2, x3)) MARK(U23(s(z0), x1, x2, x3)) -> c24(MARK(s(z0))) MARK(take(x0, zeros)) -> c25(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c25(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0, z1))) -> c25(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c25(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U21(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U22(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, U23(z0, z1, z2, z3))) -> c25(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c25(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c25(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c25(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0, z1), x1)) -> c25(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(U12(z0, z1))) MARK(take(length(z0), x1)) -> c25(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U21(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(U21(z0, z1, z2, z3))) MARK(take(U22(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(U22(z0, z1, z2, z3))) MARK(take(U23(z0, z1, z2, z3), x1)) -> c25(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(U23(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c25(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(s(z0), x1)) -> c25(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c25(MARK(x0)) MARK(take(x0, tt)) -> c25(MARK(x0)) MARK(take(x0, s(z0))) -> c25(MARK(x0)) MARK(take(x0, nil)) -> c25(MARK(x0)) MARK(take(zeros, x1)) -> c25(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c25(MARK(cons(z0, z1))) MARK(take(x0, U11(z0, z1))) -> c26(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0, z1))) -> c26(A__TAKE(mark(x0), a__U12(mark(z0), z1)), MARK(U12(z0, z1))) MARK(take(x0, length(z0))) -> c26(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U21(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U21(mark(z0), z1, z2, z3)), MARK(U21(z0, z1, z2, z3))) MARK(take(x0, U22(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U22(mark(z0), z1, z2, z3)), MARK(U22(z0, z1, z2, z3))) MARK(take(x0, U23(z0, z1, z2, z3))) -> c26(A__TAKE(mark(x0), a__U23(mark(z0), z1, z2, z3)), MARK(U23(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c26(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c26(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(zeros, x1)) -> c26(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c26(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0, z1), x1)) -> c26(A__TAKE(a__U12(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c26(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U21(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U22(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U22(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(U23(z0, z1, z2, z3), x1)) -> c26(A__TAKE(a__U23(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c26(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c26(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c26(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, s(z0))) -> c26(MARK(s(z0))) MARK(take(cons(z0, z1), x1)) -> c26(MARK(x1)) MARK(take(0, x1)) -> c26(MARK(x1)) MARK(take(tt, x1)) -> c26(MARK(x1)) MARK(take(nil, x1)) -> c26(MARK(x1)) A__U12(tt, U11(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U12(tt, U11(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__U12(mark(z0), z1), x1)), MARK(U11(U12(z0, z1), x1))) A__U12(tt, U11(length(z0), x1)) -> c4(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U12(tt, U11(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U11(U21(z0, z1, z2, z3), x1))) A__U12(tt, U11(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U11(U22(z0, z1, z2, z3), x1))) A__U12(tt, U11(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U11(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U11(U23(z0, z1, z2, z3), x1))) A__U12(tt, U11(take(z0, z1), x1)) -> c4(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U12(tt, U11(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U12(tt, U11(tt, x1)) -> c4(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U12(tt, U11(s(z0), x1)) -> c4(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U12(tt, U11(x0, z1)) -> c4(MARK(U11(x0, z1))) A__U12(tt, U11(0, x1)) -> c4(A__LENGTH(a__U11(0, x1))) A__U12(tt, U11(nil, x1)) -> c4(A__LENGTH(a__U11(nil, x1))) A__U12(tt, U12(U11(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U11(mark(z0), z1), x1)), MARK(U12(U11(z0, z1), x1))) A__U12(tt, U12(U12(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__U12(mark(z0), z1), x1)), MARK(U12(U12(z0, z1), x1))) A__U12(tt, U12(length(z0), x1)) -> c4(A__LENGTH(a__U12(a__length(mark(z0)), x1)), MARK(U12(length(z0), x1))) A__U12(tt, U12(U21(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U21(mark(z0), z1, z2, z3), x1)), MARK(U12(U21(z0, z1, z2, z3), x1))) A__U12(tt, U12(U22(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U22(mark(z0), z1, z2, z3), x1)), MARK(U12(U22(z0, z1, z2, z3), x1))) A__U12(tt, U12(U23(z0, z1, z2, z3), x1)) -> c4(A__LENGTH(a__U12(a__U23(mark(z0), z1, z2, z3), x1)), MARK(U12(U23(z0, z1, z2, z3), x1))) A__U12(tt, U12(take(z0, z1), x1)) -> c4(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)), x1)), MARK(U12(take(z0, z1), x1))) A__U12(tt, U12(cons(z0, z1), x1)) -> c4(A__LENGTH(a__U12(cons(mark(z0), z1), x1)), MARK(U12(cons(z0, z1), x1))) A__U12(tt, U12(tt, x1)) -> c4(A__LENGTH(a__U12(tt, x1)), MARK(U12(tt, x1))) A__U12(tt, U12(s(z0), x1)) -> c4(A__LENGTH(a__U12(s(mark(z0)), x1)), MARK(U12(s(z0), x1))) A__U12(tt, U12(x0, z1)) -> c4(MARK(U12(x0, z1))) A__U12(tt, U12(0, x1)) -> c4(A__LENGTH(a__U12(0, x1))) A__U12(tt, U12(nil, x1)) -> c4(A__LENGTH(a__U12(nil, x1))) A__U12(tt, length(zeros)) -> c4(A__LENGTH(a__length(a__zeros)), MARK(length(zeros))) A__U12(tt, length(U11(z0, z1))) -> c4(A__LENGTH(a__length(a__U11(mark(z0), z1))), MARK(length(U11(z0, z1)))) A__U12(tt, length(U12(z0, z1))) -> c4(A__LENGTH(a__length(a__U12(mark(z0), z1))), MARK(length(U12(z0, z1)))) A__U12(tt, length(length(z0))) -> c4(A__LENGTH(a__length(a__length(mark(z0)))), MARK(length(length(z0)))) A__U12(tt, length(U21(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U21(mark(z0), z1, z2, z3))), MARK(length(U21(z0, z1, z2, z3)))) A__U12(tt, length(U22(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U22(mark(z0), z1, z2, z3))), MARK(length(U22(z0, z1, z2, z3)))) A__U12(tt, length(U23(z0, z1, z2, z3))) -> c4(A__LENGTH(a__length(a__U23(mark(z0), z1, z2, z3))), MARK(length(U23(z0, z1, z2, z3)))) A__U12(tt, length(take(z0, z1))) -> c4(A__LENGTH(a__length(a__take(mark(z0), mark(z1)))), MARK(length(take(z0, z1)))) A__U12(tt, length(cons(z0, z1))) -> c4(A__LENGTH(a__length(cons(mark(z0), z1))), MARK(length(cons(z0, z1)))) A__U12(tt, length(s(z0))) -> c4(A__LENGTH(a__length(s(mark(z0)))), MARK(length(s(z0)))) A__U12(tt, length(x0)) -> c4(MARK(length(x0))) A__U12(tt, length(0)) -> c4(A__LENGTH(a__length(0))) A__U12(tt, length(tt)) -> c4(A__LENGTH(a__length(tt))) A__U12(tt, length(nil)) -> c4(A__LENGTH(a__length(nil))) A__U12(tt, U21(zeros, x1, x2, x3)) -> c4(A__LENGTH(a__U21(a__zeros, x1, x2, x3)), MARK(U21(zeros, x1, x2, x3))) A__U12(tt, U21(U11(z0, z1), x1, x2, x3)) -> 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MARK(U11(U21(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U21(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U21(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U21(take(z0, z1), x1, x2, x3))) MARK(U11(U21(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U21(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U21(cons(z0, z1), x1, x2, x3))) MARK(U11(U21(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U21(tt, x1, x2, x3), x4), MARK(U21(tt, x1, x2, x3))) MARK(U11(U21(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U21(s(mark(z0)), x1, x2, x3), x4), MARK(U21(s(z0), x1, x2, x3))) MARK(U11(U21(x0, z1, z2, z3), x4)) -> c19(MARK(U21(x0, z1, z2, z3))) MARK(U11(U21(0, x1, x2, x3), x4)) -> c19(A__U11(a__U21(0, x1, x2, x3), x4)) MARK(U11(U21(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U21(nil, x1, x2, x3), x4)) MARK(U11(U22(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__zeros, x1, x2, x3), x4), MARK(U22(zeros, x1, x2, x3))) MARK(U11(U22(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U11(z0, z1), x1, x2, x3))) MARK(U11(U22(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U22(U12(z0, z1), x1, x2, x3))) MARK(U11(U22(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__length(mark(z0)), x1, x2, x3), x4), MARK(U22(length(z0), x1, x2, x3))) MARK(U11(U22(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U22(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U22(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U22(take(z0, z1), x1, x2, x3))) MARK(U11(U22(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U22(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U22(cons(z0, z1), x1, x2, x3))) MARK(U11(U22(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U22(tt, x1, x2, x3), x4), MARK(U22(tt, x1, x2, x3))) MARK(U11(U22(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U22(s(mark(z0)), x1, x2, x3), x4), MARK(U22(s(z0), x1, x2, x3))) MARK(U11(U22(x0, z1, z2, z3), x4)) -> c19(MARK(U22(x0, z1, z2, z3))) MARK(U11(U22(0, x1, x2, x3), x4)) -> c19(A__U11(a__U22(0, x1, x2, x3), x4)) MARK(U11(U22(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U22(nil, x1, x2, x3), x4)) MARK(U11(U23(zeros, x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__zeros, x1, x2, x3), x4), MARK(U23(zeros, x1, x2, x3))) MARK(U11(U23(U11(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U11(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U11(z0, z1), x1, x2, x3))) MARK(U11(U23(U12(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U12(mark(z0), z1), x1, x2, x3), x4), MARK(U23(U12(z0, z1), x1, x2, x3))) MARK(U11(U23(length(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__length(mark(z0)), x1, x2, x3), x4), MARK(U23(length(z0), x1, x2, x3))) MARK(U11(U23(U21(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U21(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U21(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U22(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U22(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U22(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(U23(z0, z1, z2, z3), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__U23(mark(z0), z1, z2, z3), x1, x2, x3), x4), MARK(U23(U23(z0, z1, z2, z3), x1, x2, x3))) MARK(U11(U23(take(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(a__take(mark(z0), mark(z1)), x1, x2, x3), x4), MARK(U23(take(z0, z1), x1, x2, x3))) MARK(U11(U23(cons(z0, z1), x1, x2, x3), x4)) -> c19(A__U11(a__U23(cons(mark(z0), z1), x1, x2, x3), x4), MARK(U23(cons(z0, z1), x1, x2, x3))) MARK(U11(U23(tt, x1, x2, x3), x4)) -> c19(A__U11(a__U23(tt, x1, x2, x3), x4), MARK(U23(tt, x1, x2, x3))) MARK(U11(U23(s(z0), x1, x2, x3), x4)) -> c19(A__U11(a__U23(s(mark(z0)), x1, x2, x3), x4), MARK(U23(s(z0), x1, x2, x3))) MARK(U11(U23(x0, z1, z2, z3), x4)) -> c19(MARK(U23(x0, z1, z2, z3))) MARK(U11(U23(0, x1, x2, x3), x4)) -> c19(A__U11(a__U23(0, x1, x2, x3), x4)) MARK(U11(U23(nil, x1, x2, x3), x4)) -> c19(A__U11(a__U23(nil, x1, x2, x3), x4)) MARK(U11(take(x0, zeros), x2)) -> c19(A__U11(a__take(mark(x0), a__zeros), x2), MARK(take(x0, zeros))) MARK(U11(take(x0, U11(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U11(mark(z0), z1)), x2), MARK(take(x0, U11(z0, z1)))) MARK(U11(take(x0, U12(z0, z1)), x2)) -> c19(A__U11(a__take(mark(x0), a__U12(mark(z0), z1)), x2), MARK(take(x0, U12(z0, z1)))) MARK(U11(take(x0, 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MARK(U11(take(x0, s(z0)), x2)) -> c19(A__U11(a__take(mark(x0), s(mark(z0))), x2), MARK(take(x0, s(z0)))) MARK(U11(take(x0, nil), x2)) -> c19(A__U11(a__take(mark(x0), nil), x2), MARK(take(x0, nil))) MARK(U11(take(zeros, x1), x2)) -> c19(A__U11(a__take(a__zeros, mark(x1)), x2), MARK(take(zeros, x1))) MARK(U11(take(U11(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U11(mark(z0), z1), mark(x1)), x2), MARK(take(U11(z0, z1), x1))) MARK(U11(take(U12(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__U12(mark(z0), z1), mark(x1)), x2), MARK(take(U12(z0, z1), x1))) MARK(U11(take(length(z0), x1), x2)) -> c19(A__U11(a__take(a__length(mark(z0)), mark(x1)), x2), MARK(take(length(z0), x1))) MARK(U11(take(U21(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U21(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U21(z0, z1, z2, z3), x1))) MARK(U11(take(U22(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U22(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U22(z0, z1, z2, z3), x1))) MARK(U11(take(U23(z0, z1, z2, z3), x1), x2)) -> c19(A__U11(a__take(a__U23(mark(z0), z1, z2, z3), mark(x1)), x2), MARK(take(U23(z0, z1, z2, z3), x1))) MARK(U11(take(take(z0, z1), x1), x2)) -> c19(A__U11(a__take(a__take(mark(z0), mark(z1)), mark(x1)), x2), MARK(take(take(z0, z1), x1))) MARK(U11(take(cons(z0, z1), x1), x2)) -> c19(A__U11(a__take(cons(mark(z0), z1), mark(x1)), x2), MARK(take(cons(z0, z1), x1))) MARK(U11(take(0, x1), x2)) -> c19(A__U11(a__take(0, mark(x1)), x2), MARK(take(0, x1))) MARK(U11(take(tt, x1), x2)) -> c19(A__U11(a__take(tt, mark(x1)), x2), MARK(take(tt, x1))) MARK(U11(take(s(z0), x1), x2)) -> c19(A__U11(a__take(s(mark(z0)), mark(x1)), x2), MARK(take(s(z0), x1))) MARK(U11(take(nil, x1), x2)) -> c19(A__U11(a__take(nil, mark(x1)), x2), MARK(take(nil, x1))) MARK(U11(take(x0, x1), x2)) -> c19(MARK(take(x0, x1))) A__U12(tt, U11(zeros, x1)) -> c4(A__LENGTH(a__U11(a__zeros, x1))) MARK(U11(U11(zeros, x1), x2)) -> c19(A__U11(a__U11(a__zeros, x1), x2)) MARK(U12(U11(U11(z0, z1), x1), x2)) -> 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c22(A__U21(a__U11(s(mark(z0)), x1), x2, x3, x4), MARK(U11(s(z0), x1))) MARK(U21(U11(x0, z1), x2, x3, x4)) -> c22(MARK(U11(x0, z1))) MARK(U21(U11(zeros, x1), x2, x3, x4)) -> c22(A__U21(a__U11(a__zeros, x1), x2, x3, x4)) MARK(U21(U11(0, x1), x2, x3, x4)) -> c22(A__U21(a__U11(0, x1), x2, x3, x4)) MARK(U21(U11(nil, x1), x2, x3, x4)) -> c22(A__U21(a__U11(nil, x1), x2, x3, x4)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_2, a__U21_4, a__U22_4, a__U23_4, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_4, A__U22_4, A__U23_4, A__LENGTH_1, A__TAKE_2, MARK_1, A__U12_2 Compound Symbols: c2_1, c6_1, c8_1, c10_1, c13_1, c16_1, c27_1, c30_1, c4_2, c4_1, c19_1, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c19_2, c20_2